Question

Q 16: Solve the following linear programming problem graphically:

Maximize

Z = 6x + 3y

Subject to the following constraints:

4x + y 2 80

x + 5y 2 115

3x + 2y < 150 x 2 0, y 20​

Answer 1

Answer:

Maximum value of Z=6x+4y=16.

Step-by-step explanation:

To Maximize: Z=6x+4y  

Constraints: x≤2  

 x+y≤3  

  −2x+y≤1

  x≥0,y≥0

Plotting the constraints on the graph, we get the following points.

Points  Z=6x+4y  

O(0,0) 0  ← Minimum

B(2\3,7\3) 40\3

C(2,1) 16  ← Maximum

D(2,0) 12  

Hence, at C≡(2,1), Maximum value of Z=6x+4y=16.