Let the manufacturer manufacture x and y numbers of type 1 and type 2 trunks.
∴According to the question,
3X + 3y ≤ 18, 3x + 2y ≤ 15, x ≥ 0, y ≥ 0
Maximize Z = 30x + 25y
The feasible region determined 3X + 3y ≤ 18, 3x + 2y ≤ 15, x ≥ 0, y ≥ 0 is given by
The corner points of feasible region are A(0,0) , B(0,6) , C(3,3) , D(5,0).
The value of Z at corner point is
Corner Point |
Z = 30x + 25y |
|
A(0, 0) |
0 |
|
B(0, 6) |
150 |
|
C(3, 3) |
165 |
Maximum |
D(5, 0) |
150 |
|
The maximum value of Z is165 and occurs at point (3,3).
The manufacturer should manufacture 3 trunks of each type to earn maximum profit of Rs.165.