Given the linear program Max 3A 4B st 1A 2B

Given the linear program

Max 3A + 4B
s.t.
-1A + 2B <= 8
1A + 2B <= 12
2A + 1B <= 16
A, B =>0

a.) Write the problem in standard form
b.) Solve the problem using the graphical solution procedure.
c.) What are the values of the three slack variables at the optimal solution?

Solution

given the linear program
Max 3A + 4B
s.t.
-1A + 2B ? 8
1A + 2B ? 12
2A + 1B ? 16
A,B ? 0

a. Write the problem in standard form.

Maximize 3A + 4B
subject to
1A - 2B ? 8
1A + 2B ? 12
2A + 1B ? 16
A,B ? 0

b. Solve the problem using the graphical solution procedure.

You have to graph these on graph paper using the x axis as A and the y axis as B

Graph the constraints, all in first quadrant since A?0 and B?0

The linear program had to be entered in this form

maximize p = 3x + 4y
subject to
x - 2y <= 8
x + 2y <= 12
2x + y <= 16
x >= 0
y >= 0

c. What are the values of the three slack variables at the optimal solution?

Since optimum occurs when A=20/3 and B=8/3

The value of the first constraint left side is -4/3
The value of the second constraint left side is 12
The value of the third constraint left side is 16