Question

A small firm manufactures gold rings and chains. The combined number of rings and chains manufactured per day is at most 24. It takes 1 hour to make a ring and half an hour for a chain. The maximum number of hour to available per day is 16. If the profit on a ring is ₹300 and that on a chain is ₹190, how many of each should be manufactured daily so as to maximize the profit?

Answer 1

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.