The two types of linear programming discussed.

Five examples of LP applications.

Four Requirements for LP problems.

ISO Profit Solution Method.

Corner Point Solution Method.

Linear Programming Homework Problem
B.1
Solve the following linear programming problem graphically:
Maximize Profit P = 4 X + 6Y
Subject to: X + 2Y < = 8 5X + 4Y < = 20 X, Y > = 0

• B.2
Solve the following linear programming problem graphically:
Maximize Profit P = X + 10Y
Subject to: 4X + 3Y < = 36 2X + 4Y < = 40 Y < = 3 X, Y > = 0

Ans:

The above figure illustrates the constraints given in the problem:
1st Corner-point is (X = 0, Y = 0) Profit = 0
2nd Corner-point is (X = 4, Y = 0) Profit = 4(4) + 6(0) = 16
3rd Corner-point is (X = 1.33, Y = 3.33) Profit = 4(1.33) + 6(3.33) = 25.33
4th Corner-point is (X = 0, Y = 4) Profit = 4(0) + 6(4) = 24
3rd Corner-point is obtained by solving equations X + 2Y = 8 & 5X + 4Y = 20 simultaneously. Multiply the first equation by 2 and subtract it from the 2nd.
We get 3X = 4  or  X=  1.33
Now, we substitute the value of X in the 1st equation, we get –

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