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Question Power Systems
1. Consider a three-phase power system with one-line diagram shown in Figure 1. The three-phase trans- former between CBs 1 and 2 (CB: circuit breaker) nameplate ratings are listed: 5MVA, 13.8A-138.0YkV, the transformer reactance X₁1 = 3.80 (viewed from low voltage side 13.8kV, resistance is negligible). The impedance of the transmission line between CBs 3 and 4 is ZL1 = (10+j100). -(50 pts) (a) Pick up SB = 100MVA for the entire three-phase system, and rated voltage VB = 138.0kV, calculate the per-unit line L1 and transformer impedance values. (b) If an SLG fault occurs at the midpoint of the line (L2) between CBs 5 and 6, which breaker(s) should operate? If the CB 5 or CB 6 does not operate, which breaker(s) will provide the backup protection? (c) List the operating CB(s) for different zones, which are listed in Figure 2. (d) If the second generator is connected at bus 3, the system (generators, buses, and transmission lines) is protected by overcurrent relays R1 to R12. Assuming the directional overcurrent relays are used for three transmission lines, what is the remote backup relay(s) for R7? And why? G Generator mm www Transformer - GSU Bus 1 depending on which breakfas Bus 3 Transmission line L1 Shunt Reactor L3 Shunt Capacitor Figure 1: A three-phase power system. Bus 2 Distribution Transformer Feeder
Verified AnswerQuestion Hydraulics
Q1. Calculate capillary rise/fall in a glass tube 2 mm diameter when immersed in (a) water (b) mercury.Both the liquids are at 20°C and the surface tension values at this temperature for water and mercury are 0.072 N/m and 0.052 N/m respectively. The specific gravity of mercury is 13.6. The contact angle of water and mercury are 0° and 130° respectively.
Verified AnswerQuestion Circuits
The switch in the circuit has been closed for a long time, and it is opened at t=0. Find v(t) for t>= 0. Calculate the initial energy stored in the capacitor. (a). When the switch is closed, calculate the value of Vc. (b). When the switch is opened, find the time constant. (c). Find v(t) for t>= 0. (d). Find p(t) for t>= 0. (e). Calculate the initial energy stored in the capacitor.
Verified AnswerQuestion Kinematics of Machines
• 2-40 Water is being heated in a closed pan on top of a range while being stirred by a paddle wheel. During the process, 30 kJ of heat is transferred to the water, and 5 kj of heat is lost to the surrounding air. The paddle-wheel work amounts to 500 N:m. Determine the final energy of the system if its initial energy is 12.5 kJ.
Verified AnswerQuestion Thermodynamics
3.19. An ideal gas initially at 600 K and 10 bar undergoes a four-step mechanically reversible cycle in a closed system. In step 12, pressure decreases isothermally to 3 bar; instep 23. pressure decreases at constant volume to 2 bar; in step 34, volume decreases at constant pressure; and in step 41, the gas returns adiabatically to its initial state.Take Cp = (7/2)R and Cy = (5/2)R. (a) Sketch the cycle on a PV diagram. (b) Determine (where unknown) both T and P for states 1, 2, 3, and 4. \text { (c) Calculate } Q, W, \Delta U, \text { and } \Delta H \text { for each step of the cycle. }
Verified AnswerQuestion Thermodynamics
4) Refrigerant-134a enters the condenser of a residential heat pump at 800 kPa and 35°C at a rate of 0.018 kg/s and leaves atS00 kPa as a saturated liquid. If the compressor consumes 1.2 kW of power, determine (a) the COP of the heat pump and(b) the rate of heat absorption from the outside air.
Verified AnswerQuestion Chemical Thermodynamics
E2A.6(a) A sample of 4.50g of methane occupies 12.7 dm3 at 310 K. (i) Calculate the work done when the gas expands isothermally against a constant external pressure of 200 Torr until its volume has increased by 3.3 dm². (ii) Calculate the work that would be done if the same expansion occurred reversibly. E2A.6(b) A sample of argon of mass 6.56g occupies 18.5 dm3 at 305 K.(i) Calculate the work done when the gas expands isothermally against a constant external pressure of 7.7kPa until its volume has increased by 2.5 dm3.(ii) Calculate the work that would be done if the same expansion occurred reversibly. F=\frac{k T}{2 l} \ln \left(\frac{1+v}{1-v}\right) \quad v=\frac{n}{N} where k is Boltzmann's constant, N is the total number of units, and l= 45 nm for DNA. (a) What is the magnitude of the force that must be applied to extend a DNA molecule with N=200 by 90 nm? (b) Plot the restoring force against v, noting that v can be either positive or negative. How is the variation of the restoring force with end-to-end distance different from that predicted by Hooke's law? (c) Keeping in mind that the difference in end-to-end distance from an equilibrium value is x = nl and, consequently, dx = ldn= Nldv,write an expression for the work of extending a DNA molecule. Hint: You must integrate the expression for w. The task can be accomplished best with mathematical software.
Verified AnswerQuestion Thermodynamics
2. (1-62) A mercury manometer (p = 13,600 kg/m') is connected to an air duct to measure the pressure inside. The difference in the manometer levels is 15 mm, and the atmospheric pressure is 100kPa. a. Answer in one sentence: Judging from figure below,determine if the pressure in the duct is above or below the atmospheric pressure. (Points 2) b. Determine the absolute pressure in the duct. (Points 7)
Verified AnswerQuestion General Biological Science And Research
Q3.1. Yeast have mitochondria and can perform cellular respiration. What would you expect to be consumed and produced during the process of cellular respiration in yeast? a.Glucose and O2 consumed; CO2 H20, and energy produced. b.Glucose, H2O, CO2, and energy consumed; O2 produced. c. CO2 and H2O consumed; glucose, O2, and energy produced. d. CO2 and energy consumed; H20, 02, and energy produced.
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Question Corporate Accounting
Question Balance the Accounting Equation Determine the effects of Transactions on the Accounting Equation. Instructions: Use the above format. Find all the required data in reference section. Submit solution in Excel. Handwritten solution will not be accepted.
Verified AnswerQuestion Mechanics
8:53 43 Done ezto.mheducation.com AA Problem Set 02 -... Saved Save & Exit Submit 4 Check my work 5 Part 2 of 6 0.58 points eBook Hint Print References Required information A rope connecting points A and B supports the force F shown in the figure. Write expressions using Cartesian vector representation for the following. Take L = 10 ft and F = 14 lb. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. y L B x / 1 30° F < Prev 5 6 7 9 of 17 S V 8:53 43 Done ezto.mheducation.com AA Problem Set 02 -... Saved Save & Exit Submit 4 Check my work 5 IENIESCHILOLIVII IVI LITE ! Required information Part 2 of 6 0.58 points eBook Hint Print References NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. y L x 1 30° F T BA : the position vector from B to A. (Round the final answers to four decimal places, Include a minus sign if necessary) T BA = ( + j ) ft < Prev 5 6 7 .. 9 of 17 S A E
Verified AnswerQuestion Mechanics
3. Obtain the membrane stress resultants for the axisymmetric shell whose cross-section is shown below. The shell is filled with a liquid of density y to the level indicated and the self weight of the shell is negligible. The shell is supported on a ring beam at the position shown. Sketch the distribution of the meridional resultant, Nm. A Im B CONE 3m 30° GO F SPHERE C 2m RING BEAM D
Verified AnswerQuestion Educations/Teaching
Curriculum Models Assignment Students will work to thoroughly research one of the following curriculum models; Montessori, Reggio, Emergent or High Scope and complete all of the following parts of the project. Part One (50 points)-Students will create a PowerPoint Presentation. This slideshow should include a minimum of 12-15 slides and be colorful and creative. Please include both information about the curriculum model, its history as well as pictures of actual classrooms and materials. PowerPoint slides should be creative, visually stimulating and organized in a logical manner.
Verified AnswerQuestion Matlab And Simulation
Lab Sheet 6: Performance Analysis of a Three-Phase Induction Motor Objective: Analyze and calculate various performance parameters of a three-phase, 4-pole, 200V, 400Hz induction motor. Understand the effects of electrical properties on motor performance using MATLAB, Python, or Excel. Equipment and Software: MATLAB, Python, or Excel Calculator for manual verification Motor Specifications: Type: Three-phase, 4-pole induction motor Rated Voltage: 200V Frequency: 400Hz Stator Resistance (𝑅𝑠Rs ): 1.71 ohms Stator Reactance (𝑋𝑠Xs ): 0.12 ohms Rotor Resistance (𝑅𝑟Rr ): 0.5 ohms Rotor Reactance (𝑋𝑖′Xi′ ): 0.3 ohms Magnetizing Reactance (𝑋𝑚Xm ): 32 ohms Slip (𝑠s): 2.5% Friction Losses: 100W Negligible Core Losses Tasks: Calculate the Synchronous Speed: Use the formula: 𝑛𝑠=120×𝑓𝑃ns =P120×f Where 𝑓f is the frequency, and 𝑃P is the number of poles. Calculate the Motor Speed at Full Load: Considering the slip (𝑠s), use the formula: 𝑛=𝑛𝑠×(1−𝑠)n=ns ×(1−s) Determine the Total Impedance: Combine stator impedance, rotor impedance referred to the stator, and magnetizing impedance. Use parallel and series combinations as applicable. Calculate the Stator Current and Power Factor: Use Ohm’s law and impedance to find the current: 𝐼𝑠=𝑉𝑝ℎ𝑍𝑡𝑜𝑡𝑎𝑙Is =Ztotal Vph Determine the power factor from the impedance phase angle. Compute Stator and Rotor Copper Losses: 𝑃𝑠𝑐𝑢=3×𝐼𝑠2×𝑅𝑠Pscu =3×Is2 ×Rs 𝑃𝑟𝑐𝑢=3×𝐼𝑟2×𝑅𝑟Prcu =3×Ir2 ×Rr Calculate the Air Gap Power: 𝑃𝑔𝑎𝑝=𝑃𝑟𝑐𝑢/𝑠 Determine the Developed Power and Torque: Subtract rotor copper losses from the air gap power for developed power. Calculate the torque using the developed power and motor speed. Assess Input and Output Power: Input power calculation incorporating power factor. Output power considering friction losses. Evaluate Motor Efficiency: Ratio of output power to input power, expressed as a percentage. Instructions: Students may choose MATLAB, Python, or Excel to perform the calculations. Document all steps, formulas, and intermediate values. Discuss the impact of slip, stator, and rotor resistances on motor performance. Submission: Submit all calculations, code (if applicable) and a discussion on the implications of your findings on motor design and operation. Lab Sheet for Session 5 Objective: Analyse DC motor operations using MATLAB and perform a comprehensive load analysis for an aircraft's electrical system using Excel. Materials: MATLAB software Microsoft Excel Exercise 1: DC Motor Analysis Using MATLAB A DC shunt motor connected to a 460-V supply has an armature resistance of 0.15 Ω. Calculate: (a) The back e.m.f when the armature current is 120 A. (b) The armature current when the back e.m.f. is 447.4 V. A DC shunt motor connected to a 460-V supply takes an armature current of 120 A on full load. Calculate the back e.m.f. at this load given the armature resistance of 0.25 Ω. A 4-pole DC shunt motor takes an armature current of 150 A at 440 V, with an armature resistance of 0.15 Ω. Calculate the back e.m.f. at this load. A 28 V DC motor with an armature resistance of 0.3 ohm, rated at 800 rpm and 5 A, is used to drive a pump. Calculate the no-load speed. Exercise 2: Load Analysis Using Excel Using the provided aircraft electrical data and load profiles, compute the following using Excel: The electrical data for a military aircraft is as follows: Number of generators : 2 (split bus) Number of inverter (for emergency use only) : 1 Number of Transformer Rectifier Unit : 2 Number of battery : 1 Specs: Generator Voltage 115 Frequency 400 Power Factor 0.8 Configuration WYE Max Continuous Power Rating (kVA) 15 Interval Rating (5 s – KVA 24 Interval Rating (5 min – kVA) 18 Inverter Emergency Rating (kVA) 15 Voltage (AC) 115 Frequency 400 Power Factor 0.8 Configuration WYE TRU Rating (amps) 150 Output Voltage (DC) 28 Max Continuous Power Rating (kVA) 150 Interval Rating (5 s – KVA 600 Interval Rating (5 min – kVA) 225 Battery Rating (AH) 40 Output Voltage (DC) 28 There are seven flight profiles. G1 : Start-Up G2 : Taxi G3 : Take Off and Climb G4: Cruise G5 : Landing G6: Ground Alert G7: Double Gen Failure The various AC Loads are as follows: LRU Consumption (VA) Profiles Used Operating Time Fuel Booster Pump 1800 G1, G6 Continuous Fuel Transfer Pump 1628 G1, G6,G7 Continuous Amplifier 10 G1, G3,G7 Continuous Oxygen 9 G2, G3,G4,G7 Continuous Cabin Control 23 G2, G3,G5,G6 Continuous Cockpit Lighting 167 G2, G4,G5,G6 Continuous Heat 270 G1, G2, G5,G6 Continuous Radar 2500 G1, G4, G6 Continuous Avionics Computer 170 G1,G3, G4,G6,G7 Continuous Avionics Sys 1 2700 G3, G7 Continuous Avionics Sys 2 870 G5,G7 Continuous HUD 235 G3,G4,G5 Continuous Fuel Measurement 28 G4,G5 Continuous Weapon System 400 G2, G6 Continuous EW System 3410 G1,G2, G6,G7 Continuous Nav 1` 132 G1,G2, G4,G6,G7 Continuous Nav 2 85.7 G1,G5, G4,G6,G7 Continuous GPS 98.9 G5,G6,G7 Continuous 26 V transformer 82 G2,G5 Continuous Others 4300 G3 Continuous The various DC Loads are as follows: LRU Consumption (Amps) Profiles Used Operating Time VOR/ILS 2 G1, G7 Continuous EW1 5.5 G5, G7 Continuous EW2 1.52 G2, G5,G7 Continuous Controller 0.1 G2, G5, G6 Continuous J Box 0.5 G2, G4,G5,G6 Continuous Air Con 1.8 G3, G4,G5 Continuous Cockpit Lights 4.7 G2, G3,G5,G6,G7 Continuous Anti-Collision Lights 3.4 G1, G4, G3 Continuous Formation Light 0.2 G7, G4, G3 Continuous Landing Light 16.1 G6 Continuous EFIS 2.33 G6,G7 Continuous ADAHRS 0.6 G2 Continuous Transmitter 14.28 G4,G5,G6,G7 Continuous Receiver 3.57 G2, G3,G5,G6,G7 Continuous Standby 4 G3,G5,G6,G4 Continuous Comms Panel 0.3 G4, G3,G5,G6,G7 Continuous AWS 6.9 G2, G5,G7 Continuous SMD 5 G7 Continuous Master Comp 1 G7 Continuous Others 122 G1 Continuous AC Load Analysis: For each flight profile, compute the total consumption in VA. DC Load Analysis: For each flight profile, compute the total consumption in Amps. Evaluate whether the provided generators, inverter, and TRU can cater to these loads under different flight profiles. Questions: How does the back e.m.f. affect the performance of a DC motor? What is the impact of varying the load conditions on the electrical system of an aircraft? Can the aircraft's electrical system handle all operational scenarios without overloading any component? Lab Sheet for Session 4 Objective: Explore the Fourier series representation of square waves and perform detailed harmonic power analysis for inverters in electrical circuits. Materials: Microsoft Excel software Exercise 1: Fourier Series Analysis of a Square Wave Given a square wave of amplitude 3 V and frequency 50 Hz, use MATLAB to compute the Fourier series coefficients up to the 25th harmonic. Sum up to 12th harmonics and up to 2th 5 harmonics plot the two resulting waveform. Observe which waveform (12 vs 25 harmonics) looks more like the original square wave. Questions: Which waveform resembles the original square wave more closely, and why? How does increasing the number of harmonics affect the approximation of the square wave? Exercise 2: Power Analysis for Inverter Circuits Using Excel Using Microsoft Excel, perform a detailed power analysis for a half-bridge and a full-bridge inverter under the following conditions: Load = 20 ohms, DC voltage = 20V, frequency of switching = 200 Hz. Calculate up to the 100th harmonic. Columns: Harmonic Number, Frequency, Voltage at the Harmonic, Resistance, Inductive Reactance, Impedance, Current, Power Factor, and Power. Compute Total Power, Fundamental Power, Total Harmonic Power, and Total Harmonic Distortion (THD). Repeat for the two inverters for Load = 20 ohms, L = 159 mH, DC voltage = 20V, frequency of switching = 200 Hz. Questions: How does the addition of inductance affect the power distribution across the harmonics? What implications do your findings have for the design and operation of inverter systems?
Verified AnswerQuestion Managerial Accounting
Question Create a Production budget for the Gertrude for the month of July, August and September. Assume units as constant- 1000 units. Instructions: Use Excel to create the Production Budget. Show all the calculations using excel functions and formulas. Handwritten solution will not be accepted. Do not use AI.
Verified AnswerQuestion Advanced Mathematics
Math-Help-Services.com Introduction to Polynomials 3 Shannon MacLean Question 1 Question 3 Which of the following polynomials are written with their Indicate the degree of the polynomial given below. terms in the proper order? 1. 4x-1 2. x4 - 4x2 3. 2x+5x2 + 9×4 16x+4-x2 Question 4 Indicate the degree of the polynomial given below. Question 2 Which of the following polynomials are written with their terms in the proper order? 7-5x2 -12x -- 1. 3x2 -> + 5x4 + 10 2. 4x3 - x2 +9x-7 3. 5x3 -x+12 Question 5 indicate the degree of the polynomial given below. 9+5x4 http://math-help-services.org 20/04/2018 09:42:46 Page 1 of 3 Math-Help-Services.com 8 Question 6 Which of the following polynomials are written with their terms in the proper order? Question 8 Which of the following polynomials are written with their terms in the proper order? 1. x - x4 -x3 2. 7x-4x2 -2x4 3. 5x+ +9x2 - 8 1. x2 - 4 2. 5x2 - x-15x4 3. 81-x4 Question 7 Question 9 Which of the following polynomials are written with their terms in the proper order? Indicate the degree of the polynomial given below. 6x-5x3 http://math-help-services.org 20/04/2018 09:42:46 Page 2 of 3 1. 6x5 -3x4 -x3 2. 2x4 +7x- 422 - x3 3. 3x2 + 7x4 -12x6 9 Math-Help-Services.com Question 10 Which of the following polynomials are written with their terms in the proper order? 1. x3 -7x2 + 12x 2. x2 - 19+ 11x3 3. x+1 http://math-help-services.org 20/04/2018 09:42:46 Page 3 of 3 10 Math-Help-Services.com Introduction to Polynomials 3 Shannon MacLean - MTH-S42 Module 1 (16719) Answer Sheet Question 1 1 and 2 only Question 2 2 and 3 only Question 3 2 Question 4 2 Question 5 4 Question 6 3 only Question 7 1 only Question 8 1 only Question 9 3 Question 10 1 and 3 only - http://math-help-services.org 20/04/2018 09:42:46 Page 1 of 1
Verified AnswerQuestion Advanced Mathematics
Math-Help-Services.com Introduction to Polynomials 1 Shannon MacLean Question 1 Combine the like terms of the polynomial given below and identify the leading coefficient of the resulting polynomial. Question 4 Identify the variable and the constant in the polynomial given below. 2-x2 +3x2 - 4x+2x +6+ 4x2 = ? 9x3 +5x2 - 5 Question 2 Combine the like terms of the polynomial given below and identify the leading coefficient of the resulting polynomial. Question 5 Combine the like terms of the polynomial given below and. identify the leading coefficient of the resulting polynomial. 2x2 -2 -3+2x+6+4x2 -10-2 = ? Question 3 Combine the like terms of the polynomial given below and identify the leading coefficient of the resulting polynomial. Question 6 Combine the like terms of the polynomial given below and identify the leading coefficient of the resulting polynomial. 3x2 +5x+6-2x2 +2x-1 =? 2×3 -3x-2x3 - 1+3x+52 - 1 =? 9x3 -x-2x3 - 1+3x+5x2 - 5 =? http:/math-help-services.org 20/04/2018 09:39:56 Page 1 of 2 Math-Help-Services.com Question 7 Combine the like terms of the polynomial given below and identify the leading coefficient of the resulting polynomial. Question 9 Identify the variable and the constant in the polynomial given below. 4-3x2 +x+5-4x+ 7x2 = ? ₹ -4x+5 Question 8 Combine the like terms of the polynomial given below and identify the leading coefficient of the resulting polynomial. Question 10 Combine the like terms of the polynomial given below and identify the leading coefficient of the resulting polynomial. ≥ +3x+2x3 +4+23 - 2x2 -3x+6 =? 2x3 +5% +2x-62 -1 =? http://math-help-services.org 20/04/2018 09:39:57 Page 2 of 2 Math-Help-Services.com Introduction to Polynomials 1 Shannon MacLean - MTH-S42 Module 1 (16719) Answer Sheet Question 1 6x2 - 2x+8 leading coefficient is 6 Question 2 7x3 + 5x2 + 2x-6 leading coefficient is 7 Question 3 5x2 -2 leading coefficient is 5 Question 4 variable is x constant is - 5 Question 5 -2x3 +6x2 +2x-7 leading coefficient is - 2 Question 6 x +7x+5 leading coefficient is 1 Question 7 4x2 - 3x+ 9 leading coefficient is 4 Question 8 4x3 - 2 + 10 leading coefficient is 4 Question 9 variable is x constant is 5 Question 10 2x3 - x2 +2x-1 leading coefficient is 2 http:/math-help-services.org 20/04/2018 09:39:57 Page 1 of 1 3
Verified AnswerQuestion Advanced Mathematics
Math-Help-Services.com Introduction to Polynomials 1 Shannon MacLean Question 1 Combine the like terms of the polynomial given below and identify the leading coefficient of the resulting polynomial. Question 4 Identify the variable and the constant in the polynomial given below. 2-x2 +3x2 - 4x+2x +6+ 4x2 = ? 9x3 +5x2 - 5 Question 2 Combine the like terms of the polynomial given below and identify the leading coefficient of the resulting polynomial. Question 5 Combine the like terms of the polynomial given below and. identify the leading coefficient of the resulting polynomial. 2x2 -2 -3+2x+6+4x2 -10-2 = ? Question 3 Combine the like terms of the polynomial given below and identify the leading coefficient of the resulting polynomial. Question 6 Combine the like terms of the polynomial given below and identify the leading coefficient of the resulting polynomial. 3x2 +5x+6-2x2 +2x-1 =? 2×3 -3x-2x3 - 1+3x+52 - 1 =? 9x3 -x-2x3 - 1+3x+5x2 - 5 =? http:/math-help-services.org 20/04/2018 09:39:56 Page 1 of 2 Math-Help-Services.com Question 7 Combine the like terms of the polynomial given below and identify the leading coefficient of the resulting polynomial. Question 9 Identify the variable and the constant in the polynomial given below. 4-3x2 +x+5-4x+ 7x2 = ? ₹ -4x+5 Question 8 Combine the like terms of the polynomial given below and identify the leading coefficient of the resulting polynomial. Question 10 Combine the like terms of the polynomial given below and identify the leading coefficient of the resulting polynomial. ≥ +3x+2x3 +4+23 - 2x2 -3x+6 =? 2x3 +5% +2x-62 -1 =? http://math-help-services.org 20/04/2018 09:39:57 Page 2 of 2 Math-Help-Services.com Introduction to Polynomials 1 Shannon MacLean - MTH-S42 Module 1 (16719) Answer Sheet Question 1 6x2 - 2x+8 leading coefficient is 6 Question 2 7x3 + 5x2 + 2x-6 leading coefficient is 7 Question 3 5x2 -2 leading coefficient is 5 Question 4 variable is x constant is - 5 Question 5 -2x3 +6x2 +2x-7 leading coefficient is - 2 Question 6 x +7x+5 leading coefficient is 1 Question 7 4x2 - 3x+ 9 leading coefficient is 4 Question 8 4x3 - 2 + 10 leading coefficient is 4 Question 9 variable is x constant is 5 Question 10 2x3 - x2 +2x-1 leading coefficient is 2 http:/math-help-services.org 20/04/2018 09:39:57 Page 1 of 1 3
Verified AnswerQuestion Matlab And Simulation
Assignment 1 (10 marks) There are two questions in this assignment: Question 1 is an LP problem, Question 2 is an NLP problem. Hint: First establish the mathematical model based on the lecture slides. Then get start with MATLAB. Get familiar with the MATLAB program codes provided, L1_ex1_1_simple.m and L1_ex1_3_simple.m or L1_ex1_1_standard.m and L1_ex1_3_standard.m. The simple version of these two codes do not include how to plot the feasible areas and are therefore more suitable for students who are not very familiar with MATLAB. Try to understand the functions in the programs by using MATLAB online help and reading the necessary document. Then obtain the graphical solutions to the following two questions by making necessary changes to the codes. Please go to the tutorial classes to know more about MATLAB, the modelling, and the detailed requirements. You must complete the MATLAB quiz in Week 0 before submitting Assignment 1, otherwise your assignment will be marked as a 0. Question 1: The local bookstore must determine how many of each of the four new books on photonics it must order to satisfy the new interest generated in the discipline. Book 1 costs $50, will provide a profit of $10, and requires 3 inches of shelf space. Book 2 costs $70, will provide a profit of $12, and requires 8 inches of shelf space. Book 3 costs $80, will provide a profit of $8, and requires 2 inch of shelf space. Book 4 costs $65, will provide a profit of $15, and requires 2 inches of shelf space. Find the number of each type that must be ordered to maximize profit. Total shelf space is 620 inches. Total amount available for ordering is $9500. It has been decided to order at least 20 Book 3. (1) Establish the model of the optimisation problem. State clearly in words what the decision variables are, what the objective function and the equation/inequality constraints represent. (2) Suppose the number of Book 3 is half the number of Book 1, and the number of Book 4 is fixed as 13, establish the model of the new optimisation problem. (3) For the model established in step (2), obtain the graphical solution using MATLAB. (4) Change one of the parameters to cause the optimal solution (optimal design variables) changes and solve the problem again. 1 Question 2: Determine the objective function for building a minimum-cost cylindrical tank of volume 60m3 and the height should be at least 2m longer than the radius, it should be noted that the cylindrical tank does not have a lid. If the circular ends cost $12 per m2 , the cylindrical wall costs $5 per m2 , the reinforcement cost for the base is $20 per m2, and it costs $30 per m2 for the protecting material over the whole surface (double sides). Additionally, the base requires an extra 10% of its total cost for transportation and installation fees. (1) Establish the mathematical model of the optimisation problem. State clearly in words what the decision variables are, what the objective function and the equation/inequality constraints represent. (2) Draw the graphs and find the optimal solution (graphical solution). (3) Change one of the parameters to cause the optimal solution (optimal design variables) changes and solve the problem again. (4) If this tank needs a lid, rebuild the mathematical model and solve the problem again. 2 Assignment 1 Submission Guide · Attempt two questions: one linear programming problem (questions 1) and one non- linear programming problem (questions 2). · Write a short report in PDF document format. Submit the written code separately (MATLAB scripts) for each question you have attempted along with the report. Make sure to name the files with the question number and name the MATLAB script (.m extension file) with your student ID. Submit the files to Canvas TurnItIn using the multiple file upload option. For example, the three files could be: Assignment_1_DOM_13123456.PDF, Qestion_1_DOM_13123456.m and Qestion_2_DOM_13123456.m . File Upload Text Entry Upload a file, or choose a file you've already uploaded. File: Choose file No file chosen PDF report + Add Another File MATLAB scripts (.m file) Click here to find a file you've already uploaded Comments ... Cancel Submit Assignment . No marks will be given if you do not upload the MATLAB scripts along with the report. · The assignment is worth 10 marks, each question is worth 5 marks. · For question1: o For sub-question (1), write the model of the optimisation problem (0.5 marks), describe the decision variables, objective function, and equality/inequality constraints (1 mark) o Solve sub-question (2) (0.5 marks) o For sub-question (3), find the optimal solution by the code of MATLAB and give an image of the graphical solution (2 marks) 3 o For sub-question (4), find the optimal solution and write the values of the design variables, objective function, and equality/inequality constraints (0.5 marks). Given the corresponding code and the image of the graphical solution (0.5 marks) · For question 2: o For sub-question (1), write the model of the optimisation problem (0.5 marks), describe the decision variables, objective function, and equality/inequality constraints (1 mark) o Solve sub-question (2), find the optimal solution by the code of MATLAB and give an image of the graphical solution (1.5 marks) o For sub-question (3), find the optimal solution and write the values of the design variables, objective function, and equality/inequality constraints (0.5 marks). Given the corresponding code and the image of the graphical solution (0.5 marks) o If this tank needs a lid, rebuild the mathematical model (0.5 marks) and solve the problem again (0.5 marks). · Include the code with proper comments in line to explain each code line that you have written to solve each question and attach it with the report. . For clarity, we might ask you to explain what you have written and how the code works. No mark will be given if you cannot explain the results and the code. . Any suspicious plagiarism will be reported to the university for further investigation. And the mark will not be given until the investigation is finished. . As stated in the subject outline, "Work submitted late without an approved extension is subject to a late penalty of 10 per cent of the total available marks deducted per calendar day that the assessment is overdue (e.g. if an assignment is out of 40 marks, and is submitted (up to) 24 hours after the deadline without an extension, the student will have four marks deducted from their awarded mark). Work submitted after five calendar days is not accepted and a mark of zero is awarded". 4
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Student
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