# 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. - Mathematics

Sum

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.

#### Solution

 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).

Concept: Introduction of Linear Programming
Is there an error in this question or solution?