Question

A company produces two products on two machines.

•A unit of Product 1 requires 2 hrs on machine 1 and 1 hr on machine 2.

•For Product 2, a unit requires 1 hr on machine 1 and 3 hrs on machine 2.

•The profitper unit of Products 1 and 2 are $30 and $20, respectively.

•The total weeklyprocessing time available for each machine is 80hrs.

Question 1: Let x be the number of units produced for Product 1 and y be the number of units produced for Product 2. Formulate an LP model that optimizes the company's profit.

Question 2: Is it feasible to produce 30units of Product 1 and 20units of Product 2? If yes, whichconstraints are binding? What are the slack values foreach of the constraints?

Question 3: Is it feasible to produce 30units of Product 1 and 16units of Product 2? If yes,which constraints are binding? What are the slack values foreach of the constraints?

Question 4: Consider the graphical solutiongiven in Figure 1and the points A, B, C, D, E and F. Which points areextreme points (i.e. corner points)of the feasible region? Which pointis optimal? Explain.

Answer 1

Answer 1: Let us summarize the given question as per below table:

Particulars	Product 1	Product 2
Time required on Machine 1	2 Hrs	1 Hr	(Total 80 Hrs Per Week)
Time required on Machine 2	1 Hr	3 Hr	(Total 80 Hrs Per Week)
Profit Per Unit	30 $	20 $

Let x and y be the no. of units produced for Product 1 and Product 2 respectively, then the LP model can be given as below

Objective Function = Maximize_z = 30x + 20y (Profit Maximization)

Subject to the constraints,

2x + y ≤ 80	(Machine 1)
x + 3y ≤ 80	(Machine 2)
Where, x, y ≥ 0	(Non-Negativity Condition)