Answer to Question #267645 in Operations Research for Nonny

Question

Solve using algebraic method

z = 3000x + 5000y

2x + y <= 16

x + 2y <= 11

x + 3y <= 15

Answer 1

Solution:

Algebraic method is graphical method in LPP.

Assume we have to maximize z = 3000x + 5000y

2x + y $\le$ 16

x + 2y $\le$ 11

x + 3y $\le$ 15

Plotting these inequations on graph:

ABCD is the feasible region.

At A(0,5), z = 3000(0) + 5000(5) = 15000

At B(3,4), z = 3000(3) + 5000(4) = 29000

At C(7,2), z = 3000(7) + 5000(2) = 31000 (maximum)

At D(8,0), z = 3000(8) + 5000(0) = 24000

Thus, maximum value is 31000 at x=7, y=2.