Let the firm manufacture x number of A and y number of B products.
∴According to the question,
X + y ≤ 300, 2x + y ≤ 360, x ≥ 0, y ≥ 0
Maximize Z = 5x + 3y
The feasible region determined X + y ≤ 300, 2x + y ≤ 360, x ≥ 0, y ≥ 0 is given by
The corner points of feasible region are A(0,0) , B(0,300) , C(60,240) , D(180,0).
The value of Z at corner point is
Corner Point |
Z = 5x + 3y |
|
A(0, 0) |
0 |
|
B(0, 300) |
900 |
|
C(60, 240) |
1020 |
Maximum |
D(180, 0) |
900 |
|
The maximum value of Z is 1020 and occurs at point (60,240).
The firm should produce 60 A products and 240 B products to earn maximum profit of Rs.1020.