Question

A company manufactures two types of toys A and B. A toy of type A requires 5 minutes for cutting and 10 minutes for assembling. A toy of type B requires 8 minutes for cutting and 8 minutes for assembling. There are 3 hours available for cutting and 4 hours available for assembling the toys in a day. The profit is ₹ 50 each on a toy of type A and ₹ 60 each on a toy of type B. How many toys of each type should the company manufacture in a day to maximize the profit? Use linear programming to find the solution. 

Answer 1

	Toy A	Toy B	Time in a day
Cutting time	5 min	8 min	180 min
Assembling time	10 min	8 min	240 min
Profit	50	60
Assumed quantity	x	y

Profit function z = 50x + 60y
x ≥ 0, y ≥ 0
5x + 8y ≤ 180
10x + 8y ≤ 240 or 5x + 4y ≤ 120

5x + 8y = 180

	A	B
x	0	36
y	22.5	8

5x + 4y ≤ 120

	C	D
x	0	24
y	30	0

Corner point	z = 50x + 60y
At O (0, 0)	0
At D (24, 0)	1200
At E (12, 15)	1500
At A (0, 22.5)	1350

Hence, the maximum profit is Rs 1500 at E (12, 15).