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# Graphically Solving and Maximizing Profit for Linear Programming

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Graphically solve the following problems
Maximize Profit Z= \$4X1+\$6X2
Subject to
1X1+2X2 &#8804; 8
6X1+4X2 &#8804; 24
a). What is the optimal solution?
b) If the first constraint is altered to 1X1+3X2 &#8804; 8, does the feasible region or the optimal solution change?

See attached file for full problem description.

https://brainmass.com/economics/macroeconomics/graphically-solving-maximizing-profit-linear-programming-128895

#### Solution Preview

B3
Graphically solve the following problems
Maximize Profit Z= \$4X1+\$6X2
Subject to
1X1+2X2 ≤ 8
6X1+4X2 ≤ 24
a). What is the optimal solution?
b) If the first constraint is altered to 1X1+3X2 ≤ 8, does the feasible region or the optimal solution change?

The first constraint 1X1+2X2 ≤ 8 is represented by the red line and second constraint 6X1+4X2 ≤ 24 is represented by the green line.

The optimum values of the objective function occurs at one of the extreme (corner) points of the feasible region. The coordinates of the extreme points are:

A = (0,4) B=(2,3) C=(4,0) . The Z values corresponding to the extreme points are

A = \$4*0+\$6*4 =\$24
B = \$4*2+\$6*3=\$26
C = \$4*4+\$6*0 =\$16

Thus the optimal solution occur at the point B and the maximum profit =\$ 26

b).
The first constraint 1X1+3X2 ≤ 8 is represented by the green line and second constraint 6X1+4X2 ≤ 24 is represented by the red line.

The feasible region change as shown in the graph.

The coordinates of the extreme points are (0,8/3) and (8,0)

The maximum profit Z= \$4*8 +\$6*0 =\$32

B4. Consider the following linear programming problem
Maximize Z = ...

#### Solution Summary

This solution gives the step by step method for solving linear programing problem

\$2.19