Let x and y be number of soaps be manufactured of 1st and 2nd type.
∴According to the question,
2x + 3y ≤ 480 , 3x + 5y ≤ 480, x ≥ 0, y ≥ 0
Maximize Z = 0.25x + 0.50y
The feasible region determined by 2x + 3y ≤ 480 , 3x + 5y ≤ 480, x ≥ 0, y ≥ 0 is given by
The corner points of feasible region are A(0,96) , B(0,0) , C(160,0).
The value of Z at corner points are
Corner Point |
Z = 0.25x + 0.50y |
|
A(0, 96) |
48 |
Maximum |
B(0, 0) |
0 |
|
C(160, 0) |
40 |
|
The maximum value of Z is 48 at point (0,96).
Hence, the manufacturer should make 96 soaps of the 2nd type to make maximum profit.