Question

Read the case given below carefully:

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 10 Alpha 4s and at least 15 Beta 5s produced during the production period. Alpha 4s generate $1,200 profit per unit, and Beta 5s yield $1,800 each. The company needs to determine the most profitable number of each model of smartphone to produce during the coming month.

A value- 12

B value- 15

Based on this case

a) What is the objective function? Express the objective function in mathematical terms (1 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. (1 pt.)

Answer 1

Let,

Number of Alpha 4s = x1

Number of Beta 5s = x2

Qustion – a:

Objective Function:

Here,

Objective is to maximize the profit.

Profit from Alpha 4s = $1200 per unit

Profit from Beta 5s = $1800 per unit

So Objective function is:

MAXIMIZE 1200*x1 + 1800*x2

***

Question – b:

Constraints:

Time available = 160 hours per technician which is to be utilized fully.

Number of technicians = 5

Total time available = 160*5 = 800 hours

Each Alpha 4s takes = 12 labor hours

Each Beta 5s takes = 15 hours.

So,

12*x1 + 15*x2 >= 800

At least 10 Alpha 4s and at least 15 Beta 5s is to be produced.

x1 >= 10

x2 >= 15

So, Constraints are:

12*x1 + 15*x2 = 800

x1 >= 10

x2 >= 15

Question – d:

Solving Using Solver:

Solver Parameters:

Optimal Solution:

Alpha 4s	Beta 5s
x1	x2
10	45.333

Alpha 4s = 10

Beta 5s = 45.333 (or 45 if fractional is not allowed but all the technician labor hours wont be fully utilized).

********

IF YOU HAVE ANY DOUBT, KINDLY COMMENT. I WOULD LOVE TO HELP YOU!!!

IF YOU LIKE THE ANSWER, PLEASE GIVE AN UP-VOTE OR THUMB UP. THIS WILL ENCOURAGE ME TO ANSWER MORE!!