Question

Operations Management Problem- Linear Programming

MSA Computer Corporation manufactures two models of smartphones, the Alpha 4 and the Beta 5. The firm employs five technicians, working 160 hours each per month, on its assembly line. Management insists that full employment (i.e., all 160 hours of time) be maintained for each worker during next month’s operations. It requires “A” labor hours to assemble each Alpha 4 computer and “B” labor hours to assemble each Beta 5 model. MSA wants to see at least “C” Alpha 4s and at least “D” Beta 5s produced during the production period. Alpha 4s generate “E” dollars profit per unit, and Beta 5s yield “F” dollars each. The company needs to determine the most profitable number of each model of smartphone to produce during the coming month.

Based on this case a) What is the objective function? Express the objective function in mathematical terms (2 pt)

b) What are the constraints given in the question? (i.e. ignore the constraints like all variables being positive, etc.) (3 constraints, 1 pt each, 3 pts total)

c) Solve the problem using Excel’s solver and determine the number of Alpha 4s and Beta 5s needed to be manufactured. (2 pt.)

Values are:

A= 10, B=16, C=9, D= 13, E= 1200, F= 1800

Answer 1

A = Number of Alpha 4 produce

B = Number of Beta 5 produce

(a) Objective function:

Max 1200A + 1800B

(b) Constraints:

10A + 16B <= 800 [160*5 = 800]

A >=9

B>=13

(c)

Setting this up in excel:

Initial formulation:

B C D E F I B 0 0 4 А 5 6 7 Objective 8 9 Constraint 10 1200 1800 0 LO 16 0 <= 800 9 0 1 0 0 >= 0 >= 11 1 13 12 13 14 15 16

B D E F G H 4 A B 5 0 0 1800 =SUMPRODUCT(C5:D5,C7:07) 6 7 Objective function: 1200 8 9 Constraints: 10 16 <= 800 10 1 0 =SUMPRODUCT($C$5:$D$5,09:09) =SUMPRODUCT($C$5:$D$5,C10:010) >= =SUMPRODUCT($C$5:$D$5,011:011) >= 9 11 0 1 13 12 13 14 15

Solver constraints:

Solver Parameters Set Objective: SF571 To: Max Min O Value of: 0 By Changing Variable Cells: $C$5:$D$5 Subject to the Constraints: SCS5:$D$5 = integer $F$10:$F$11 >= SH$10:SH$11 SF$9 <= SH$9 Add Change Delete Reset All Load/Save Make Unconstrained variables Non-Negative Select a Solving GRG Nonlinear Method: Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help Solve Close

Clicking solve, we get

1 А B C D E F G H 4 B 5 59 13 6 7 Objective function: 1200 1800 94200 8 9 Constraints: 10 16 798 <= 800 10 1 0 59 >= 9 11 0 1 13 >= 13 12 13

Number of Alpha 4s needed = 59

Number of beta 5s needed = 13

Total profit = $94,200

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