Let the firm manufacture x number of A and y number of B products.
∴According to the question,
X + y ≤ 24, x + 0.5y ≤ 16, x ≥ 0, y ≥ 0
Maximize Z = 300x + 160y
The feasible region determined X + y ≤ 24, x + 0.5y ≤ 16, x ≥ 0, y ≥ 0 is given by
The corner points of feasible region are A(0,0) , B(0,24) , C(8,16) , D(16,0).
The value of Z at corner point is
Corner Point |
Z = 300x + 160y |
|
A(0, 0) |
0 |
|
B(0, 24) |
3840 |
|
C(8, 16) |
4960 |
Maximum |
D(16, 0) |
4800 |
|
The maximum value of Z is 4960 and occurs at point (8,16).
The firm should produce 8 A products and 16 B products to earn maximum profit of Rs.4960.