MSA Computer Corporation manufactures three models of computers: the Alpha4, Beta5, and the Delta6. The firm employs thirteen technicians working 160 hours each per month on its assembly line. Management insists that no more than full employment on the assembly line (i.e., all 160 hours of time) can be maintained for each worker during next month’s operations, so there will be no overtime. It requires 20 labor hours to assemble each Alpha4 computer, 25 labor hours for each Beta5 model, and 15 hours for each Delta6. Final testing and inspection requires 3 hours for each Alpha4, 1.5 hours for each Beta5, and 1.2 hours for each Delta6. The company has up to 80 hours available for inspection and testing each month. Demand is such that the company can and will sell all of the computers that it produces. MSA must produce at least 10 Delta6 computers. In addition, the number of Alpha4 computers produced each month must equal or exceed the combined total of Beta5 and Delta6 computers produced. Alpha4 computers generate $1,200 profit per unit, Beta5 computers yield $1,800 each, and Delta6 computers yield $1,000 per unit. If the optimal answer is in fractions of computers that is acceptable. a) Formulate the linear programming problem to maximize the profit during the coming month. Provide the variable being used, the objective function and all of the constraints that are indicated by the above description of the problem. b) Using any available software package (POM/QM, Solver, etc.), what is the maximum profit and the quantity of each type of computer to produce. Provide your computer software input and output supporting your answers to parts a) and b). Not doing this will result in loss of 75% of the credit on this problem. If the optimal answer is in fractions of computers that is acceptable. c) Based on the computer output provided as part of part b) and not resolving the problem, provide two sensitivity analysis interpretations. One interpretation must use the objective function variables and one must use a constraint(s). Provide your supporting sensitivity analysis (ranging) output. d) Instead of the constraint that requires that MSA must produce at least 10 Delta6 computers, suppose it is now required that at least 25% of the computers produced must be Delta6 computers. Write the constraint to express this relationship. You do not need to resolve the revised linear programming formulation for the optimal answer. e) The company now wants to ensure that for every Alpha4, MSA must produce at least two Beta5. Write the constraint to express this requirement however you do not need to resolve the revised linear programming formulation for the optimal answer. 5. (23 points) The marketing department at Bodnar Industries is developing a promotional campaign to introduce a new product. A listing of the various activities required, their immediate predecessors, and estimates of their times (in days) is given below. a) Draw the precedence diagram for this network. b) Identify the critical path and the expected project completion time. c) Provide the slack time for each path relative to the critical path completion time. d) What is the probability that the critical path will be completed in more than 65 days? e) How many days should the marketing manager allow for completion of the critical path if he wants to be 99% sure that the critical path will be completed within this allowed time? Provide this answer to two decimal points (xx.xx) For any calculations that you make that involve time, use the time (days) to two decimal places (xx.xx). Activity Description Immediate Predecessors Optimistic Time Most Likely Time Pessimistic Time A Rough brochure layout — 2 3 5 B Review brochure A 6 8 10 C Final brochure layout B 4 6 8 D Final brochure artwork C 5 7 11 E Design display — 12 15 20 F Rough display artwork E 2 3 4 G Review display E 6 8 10 H Revise display G 2 3 4 I Final display artwork F,H 1 2 4 J Make display plates I 18 23 26 K Make brochure plates D,I 10 13 16 L Make and ship displays J 7 10 14 M Print and ship brochures K 6 8 10
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