Let x and y be number of gold rings and chains.
∴According to the question,
x + y ≤ 24, x + 0.5y ≤ 16x, x ≥0, y ≥ 0
Maximize Z = 300x + 190y
The feasible region determined by 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 points are
Corner Point |
Z = 300x + 190y |
|
A(0, 0) |
0 |
|
B(0, 24) |
4560 |
|
C(8, 16) |
5440 |
Maximum |
D(16, 0) |
4800 |
|
The maximum value of Z is 5440 at point (8,16).
Hence, the firm should manufacture 8 gold rings and 16 gold chains to maximize their profit.