20. A tachometer normally refers to a(n) _______ used for speed measurement. a. load cell c. ultrasonic sensor b. capacitive proximity sensor d. small generator

MATH 308 - Assignment 1 1. Find necessary and sufficient conditions for the numbers s and t to make the LP problem Maximize: f(x1, x2) = x1+x2 subject to sx1+tx2 ≤ 1 x1, x2 ≥ 0 a) have an optimal solution. b) be infeasible. c) be unbounded. Prove your answers.

25. For the programmed latching operation shown, which two instructions must have the same address? a. ON and OFF inputs. b. latch and unlatch outputs c. ON input and latch output d. OFF input and unlatch output

2. For the following product structure: a) Develop all the Bills of Material tables. b) Find the number of units of each of the raw materials (R's), components (C's),and subassemblies (S's) that are needed to make one unit of product P.

Consider the product structure of end item PR-1 given in Figure P10.1. The end-item demand from the master production schedule for the period of weeks 3, 4, 5, 6, 7, 8, 9,and 10 is 40, 30, 20, 10, 50, 30, 70, and 20 units, respectively. The manufacturing and assembly lead times for PR-1, SA-12, and C-122 and the ordering lead time for M-4 are given below. Carry out the material requirements planning procedure for raw material M-4 required to manufacture component C-122 if one unit of M-4 is required to produce one unit of C-122. Lead time for assembling PR-1 =1 week. Lead time for assembling SA-12 = 1 week.|| Lead time for manufacturing C-122 = 2 week; 100 units on-hand inventory are given and 40 units are scheduled to arrive in period 2. Procurement lead time for raw material M41 week; 40 units on-hand inventory are available.

5. A drug company sells three different formulations of vitamin complex and mineral complex. The first formulation consists entirely of vitamin complex and sells for $1 per unit. The second formulation consists of 3/4 of a unit of vitamin complex and 1/4 of a unit of mineral complex and sells for $2 per unit. The third formulation consists of 1/2 of a unit of each of the complexes and sells for $3 per unit. If the company has 100 units of vitamin complex and 75 units of mineral complex available, how many units of each formulation should the company produce as to maximize profit? Write down the corresponding LP, and solve it by using Theorem 22 and 23.

3.5-3. Ed Butler is the production manager for the Bilco Corpora- tion, which produces three types of spare parts for automobiles. The manufacture of each part requires processing on each of two machines, with the following processing times (in hours):

19. NIST SP 800-34 belongs to which contingency planning process element? a. Policy environment enabling the planning process b. Business impact analysis to understand causes and effects of precursor activities c. Planning methodologyС. d. Planning budget a nd access to resources e. None of the above

Wild West produces two types of cowboy hats. Type I hat requires twice as much labor as aType II. If all the available labor time is dedicated to Type II alone, the company can produce a total of 400 Type II hats a day. The respective market limits for the two types ofhats are 150 and 200 hats per day. The profit is $8 per Type I hat and $5 per Type II hat.The company should produce at least 100 cowboy hats (regardless of the type). Develop a reasonable mathematical model that can determine the number of hats of each type.

The Continuing Education Division at the Ozark Community College offers a total of 30 courses each semester. The courses offered are usually of two types: practical and humanistic. To satisfy the demands of the community, at least 10 courses of each type must be offered each semester. The division estimates that the revenues of offering practical and humanistic courses are approximately $1500 and $1000 per course, respectively. Develop an optimization model that can be used to find the optimal course offering plan.