# Maximization and Minimization Problems in Linear Programming

Solve the following linear programming problems graphically:

Maximize profit = 4X + 6Y

Subject to: X + 2Y ? 8

5X + 4Y ? 20

X,Y ? 0

Minimize cost = 24X + 15Y

Subject to: 7X + 11Y ? 77

16X + 4Y ? 80

X,Y ? 0

https://brainmass.com/math/graphs-and-functions/maximization-and-minimization-problems-in-linear-programming-467266

#### Solution Preview

Step by step Guide:

Maximize profit = 4X + 6Y

Subject to: X + 2Y ? 8

5X + 4Y ? 20

X,Y ? 0

For the first constraint: X + 2Y = 8

X + 2Y = 8

If Y = 0, what is the value of X?

X + 2Y = 8

X + 2(0) = 8

X + 0 = 8

X = 8

The coordinates should be stated as X, Y therefore in this case it would be (8,0).

X + 2Y = 8

If X = 0, what is the value of Y?

X + 2Y = 8

0+2Y = 8

2Y = 8

Y = 8/2

Y = 4

The coordinates would there be (0,4).

You ...

#### Solution Summary

The solutions solves maximization and minimization problems in linear programming. Graphical presentations are attached in an spreadsheet file.