Question

b) A manufacturing of UT CUver Sheet mak ng company makes two models A and B of a product. Each piece Model A requires 9 labor hours for fabricating and 1 labor hour for finishing. Each piece of Model B requires 12 labor hours for fabricating and 3 labor hours for finishing For fabricating and finishing, the maximum labor hours available are 180 and 30 respectively. The company makes a profit of AED 8000 on each piece of model A and AED 12000 on each piece of Model B. (1) Formulate the linear programming models for the above problem. (2) How many pieces of Model A and Model B should be manufactured per week to realize a maximum profit? (3) What is the maximum profit per week?

Answer 1

a)

Let a units of Model A be manufactured and b units of Model B be manufactured such that:

Maximizing Function = 8000 a + 12000 b

Such that:

9a + 12b < = 180

a + 3b < = 30

b)

I am using solver to solve the problem.

We are not allowed to upload excel. Hence uploading the screenshot of the same.

We are Maximising Profit, so our target cell would be Total Profit.

By changing cells, we would select Decision Variables (ie number of units of Model A and Model B).

And then we would add the constraints.

Below given output will be shown by solver.

Hence 12 units of Model A and 6 units of Model B should be manufactured.

The Screenshot below shows the constraints that were used

c) Profit = 8000 *12 + 12000 * 6 = 168000