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. In addition to the workers on the assembly line, 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, leave them as fractions.
a) Formulate the linear programming problem to maximize the profit during the coming month. Provide the variables 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 no more than 35% 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.