MSA Computer Corporation manufactures three models of computers: the Alpha4, Bet
ID: 429538 • Letter: M
Question
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.
Explanation / Answer
a. Let the number of Alpha4, Beta5, and the Delta6 computers made be "x", "y", "z" respectively
Profit per computer of Alpha4, Beta5, and the Delta6 are $1200, $1800, $1000 respectively.
Total profit = profit per computer*number of computers being made
= 1200x+1800y+1000z. This is the objective function and we have to maximize this function.
Constraints are:
Number of technicians = 13. No. of hours per technician = 160 hours. Total hours = 13*160 = 2080
So, (i) 20x+25y+15z<=2080 (total assembly hours should be less than or equal to the available 2080 hours)
(ii) 3x+1.5y+1.2z<=80 (total inspection time should be less than or equal to the available 80 hours)
(iii) z>=10 (at least 10 Delta6 computers must be made)
(iv) x>=y+z (number of Alpha4 computers produced each month must equal or exceed the combined total of Beta5 and Delta6 computers produced)
(b) The model is solved using solver in excel:
The input is that no. of computers cell were left blank, and the solution was calculated by excel. Formula were inserted in the cells for total profit, assembly hours, inspection time.
The input was a plain model and was:
Thus using the output model as shown at first, the no. of computers made are: alpha 4 = 18.44, beta 5 = 8.44, delta 6 = 10. maximum profit = 47,333.33
(c) sensitivity analysis (not resolving the problem). if i increase the number of delta 6 computers by 10% to 11, the profit will become: 48333.33
If i increase the assembly hours available by 10% to 2288, there will be no change in the answer.
(d) The new constraint: z>= (x+y+z)*0.25
(e) the new constraint: y>=2x
Alpha 4 Beta 5 Delta 6 No. of computers being made 18.44444 8.444444 10 Alpha 4 Beta 5 Delta 6 Profit per computer 1200 1800 1000 Total profit 47333.33 Constraints: (i) assembly hours Alpha 4 Beta 5 Delta 6 per computer 20 25 15 Total 730 <= 2080 (ii) inspection time Alpha 4 Beta 5 Delta 6 per computer 3 1.5 1.2 Total 80 <= 80 (iii) Delta 6 No. of computers being made 10 >= 10 (iv) Alpha 4 Beta 5 Delta 6 No. of computers being made 18.44444 8.444444 10 (x>=y+z)Related Questions
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