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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

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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. 

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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
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