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Q1:A consortium of Venture Capitalists are in the process of establishing a 5000 barrels per day modular Petroleum Refinery. Topping units of petroleum refineries usually have high energy demand and is furnished with train of heat exchangers and heat conservation equipment. As a member of the Process Design Team you have been tasked to present an optimal design of the topping unit which is energy efficient Develop the optimization strategy for the energy consumption and optimal operationSee Answer
Q2:1. As shown in the figure, a number of tanks are connected by pipes where, at steady state, the mass flow into and out of each tank must be equal. The rate of mass flow through each pipe is computed as the product of flow (Q) and concentration (c). As an example, the mass balance for the first tank can be written as, Q01 C01 Q31C3 = Q15C1 + Q12C1 Write mass balances for all the tanks and express the equations in matrix form. Then, use Matlab to solve for the concentrations in each tank. Q15 = 3 25 201 = 5 Q12=3 Col = 10 255 = 2 Qs4=2 Q24-1 244-11 Q23=1 24-8 Q = 1 203 = 8 C03 =20See Answer
Q3:Assignment details You are required to solve the optimisation problems below. You should produce a typed report of maximum length 4 pages. All questions must be answered in Excel, with the relevant spreadsheet(s) appended to your report as an appendix. Your report does not have to include an abstract, introduction, conclusions section etc. You are required to answer the questions. In answering each question, you should, 1. Formulate the optimisation problem; in other words, define the objective function and any associated constraints drawing on any relevant background theory, 2. Discuss the Excel implementation, 3. Show, discuss and analyse your results using any appropriate figures. Question 1 Given the following experimental data, Time, t (h) Weight, w (kg) 0.314 0.017 0.10 0.479 0.183 0.671 0.267 0.718 0.350 1.026 0.433 4.857 0.517 1.513 3.105 0.60 0.683 3.666 0.767 5.069 The following regression models have been proposed to develop a relationship between time and weight, w = exp(a] + @2 " t) w = exp(@1 + @2 . t + ag · t2) W= @1 .tªz What are the various model parameters and which model would be the most appropriate? Marking Criteria - Formulate the optimisation problem (equations and words) - Show spreadsheet implementation - professionally constructed, logical input output structure, results clearly demonstrated, model performance metrics quantified. - Discussion and quantification of model accuracy. Consideration of model performance statistics and arriving at appropriate choice of model structure. [25 marks]See Answer
Q4:Assignment details You are required to solve the optimisation problems below. You should produce a typed report of maximum length 4 pages. All questions must be answered in Excel, with the relevant spreadsheet(s) appended to your report as an appendix. Your report does not have to include an abstract, introduction, conclusions section etc. You are required to answer the questions. In answering each question, you should, 1. Formulate the optimisation problem; in other words, define the objective function and any associated constraints drawing on any relevant background theory, 2. Discuss the Excel implementation, 3. Show, discuss and analyse your results using any appropriate figures./nQuestion 2 Consider the following cascade of heat exchangers, 100ºF T. T2 500ºF * Hex 1 300ºF Hex 2 Hex 3 400ºF 600ºF + Ts T Find the minimum total surface area of the three heat exchangers. Data: mcp = 1000 (Btu . h-1 . F-1) (all streams) Exchanger U (Btu . h-1 . ft-2 . F-1) Area (ft2) Duty (Btu . h-1) 1 120 A1 Q1 2 80 A2 02 3 40 A3 Q3 Marking criteria - Formulate the optimisation problem (equations and words, justifying use of equations) - Show spreadsheet implementation - professionally constructed, logical input output structure, results clearly demonstrated. - Discussion and quantification of any uncertainty associated with the result. [25 marks]See Answer
Q5:Total budget is $4000 to spend. What is the best way to maximize profits out of the following items which need to fit on a 60" long by 30" wide table. SOLVE USING SIMPLEX METHOD Candles Cost: $4, sell $12 6" square space/unit Wigs Cost: $10, Sell for 30 10" square space/unit Hat Clips Cost: $10, Sell for $24 2" square space/unit I am pretty sure the answer comes out to 125 wigs, 275 golf clips and zero candles for standard profit maximizationSee Answer
Q6:1: Consider the following problems from the first homework. For each, derive the dual problem and illustrate that strong duality holds for these problems by finding the optimal solution to the dual (You need to find the values of the slack variables aswell!). (Hint: You do not need to use the simplex method for this problem)See Answer
Q7:4: Imagine you are a college student trying to live on a small budget. You want to minimize your food costs, but you know a diet consisting solely of instant ramen and beer may be harmful to your health. You look up recommended dietary allowance of several different nutrients to determine what you should eat to be healthy. Let i = 1...m denote the nutrients and let bi, i = 1...m denote the minimum daily requirement for each of the nutrients. Suppose make a list of your n favorite foods. Let j denote their index on your list and c; be the cost of the jh item. Let a denote the amount of the įth nutrient contained in the jth item on your food list. a: Formulate a linear problem to minimize your costs while still getting all of your daily required nutrients b: Formulate the dual to this problem c: Introduce another person to this story who is naturally interested in solving the dual problem. (Hint: Give semantic meaning to the dual problem) d: Name some real-world considerations that your model leaves outSee Answer
Q8:Green Grass, Inc. just ran out of stock and suddenly has two emergency orders for grass seed blends: one is for 1500 pounds of normal, the other for 2300 pounds of special. At least each pound of normal should contain 60 percent annual seed, while each pound of special should contain at least 70 percent perennial seed. Green Grass has two input mixtures, A and B. Mixture A contains 80 percent perennial and 15 percent annual seed. Mixture B contains 70 percent annual and 25 percent perennial seed. Mixture A costs 90 cents per pound and mixture B costs 50 cents per pound. Provide a complete LP formulation for this problem in the standard format. DO NOT SOLVE.See Answer

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