Question

The Lifang Wu Corporation manufactures two models of industrial robots, the Alpha 1 and the Beta 2. The firm employs 5 technicians, working 160 hours each per month, on its assembly line. Management insists that full employment (that is, all 160 hours of time) be maintained for each worker during next month’s operations. It requires 20 labor-hours to assemble each Alpha 1 robot and 25 labor-hours to assemble each Beta 2 model. Wu wants to see at least 10 Alpha 1s and at least 15 Beta 2s produced during the production period. Alpha 1s generate a $1,200 profit per unit, and Beta 2s yield $1,800 each.

a. How many Alpha 1's should be produced?                            [ Select ]   

b. How many Beta 2's should be produced?                            [ Select ]   

c. What is the overall profit level?                            [ Select ]

d. If the overall hours were increased by 20, how much would the profit increase?

Answer 1

Linear Programming is formulated as :

Maximize the Objective function: 1200X + 1800Y

Where

X = Number of Alpha 1 Manufactured

Y = Number of Beta 2 Manufactured

the constraints are as follows:

Labour Hours Constraints: 20X + 25Y ≤160*5 ( for 5 workers in each month)

i.e 20X + 25Y ≤ 800

X ≥ 10

Y ≥ 15

and non-negativity constraint i.e X, Y ≥ 0

Solving it using Excel's Solver :

The formulas are given as :

THE SOLVER PARAMETERS ACCORDING TO OUR PROBLEM ARE :

Hence the solution to the problem is :

a) Number of Alpha 1 = Number of X = 10

b)Number of Beta 2 = Number of Y = 24

c) Overall Profit Level = 55200 $

d)

If the overall hours available are increased by 20 to 820 :

The solution becomes

But this is not appropriate as the X, Y values can only be whole number values, as only a whole product can be sold

So the answer remains the same as c) i.e X = 10 , Y = 24 and Maximum Profit =55200 $