Question

Company X produces two types of window panes, A and B. It can only produce A at the rate of 6 per day and each requires 6 square feet of glass. It produces B at the rate of 4 per day and each requires 8 square feet of glass. However, Company can only cut 60 square feet of glass per day. It earns a profit of $300 per unit from A and $150 per unit from B. Use the simplex method to assist company X in determining how many panes of type A and B should be produced each day such that its profit is maximized.

Answer 1

Let x1,x2 be the number of products of A and B to be produced respectively.

Simplex Formulation-

Objective Function-

max 300x1+150x2

Constraints-

x1<=6

x2<=4

6x1+4x2<=60

Addition of Slack Variables to convert the above system to equations

x1+s1=6

x2+s2=4

6x1+4x2+s3=60

Initial Basic Feasible solution has x1=0 and x2=0

The Initial Table and further iterations have been attached below-