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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

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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).

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Solution Summary

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

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