Answer to Question #163557 in Operations Research for Satyam mishra

Question

Use the graphical method to solve the following LPP:

Minimize, Z = 3x + 5y

Subject to the constraints:

−3x + 4y ≤ 12

2x − y ≥ −2

2x + 3y ≥ 12

x ≤ 4; y ≥ 2 and x, y ≥ 0

Answer 1

−3x + 4y ≤ 12............i

the linear equation is represented by -3x + 4y =12

plotting equation (i) when x=0, y=3; when x=-4, y=0

2x − y ≥ −2................ii

linear equation is 2x-y=-2

when x=0, y=2; when y=0, x=-1

2x + 3y ≥ 12...............iii

linear equation 2x +3y =12

when x=0, y=4; when y=0, x=6

By minimizing;

The unshaded area satisfies the equations with the minimum coordinate (3, 2).

thus, z= 3(3) + 5(2)

= 19