A company manufactures two types of novelty ...

CBSE Class 12 Math 2020 Delhi Set 1 Solved Paper

Question : 31 of 36

Marks: +1, -0

A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A requires 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type

B

require 8 minutes each for cutting and 8 minutes each for assembling. Given that total time for cutting is 3 hours 20 minutes and for assembling 4 hours. The profit for type A souvenir is ₹ 100 each and for type B souvenir, profit is ₹ 120 each. How many souvenirs of each type should the company manufacture in order to maximize the profit? Formulate the problem as an LPP and solve it graphically.

Solution: 👈: Video Solution

Let the number of Souvenirs of type A and type B be

x

and

y

, respectively. To maximize :

Z=\text{₹}(100x+120y)

Subject to constraints :

x\ge 0

y\ge 0

5x+8y\le 200

10x+8y\le 240

Corner Points	Value of $bo Z$ (in ₹)
$A(0,25)$	3000
$B(8,20)$	$3200 \leftarrow$ Maximum
$C(24,0)$	2400

Hence maximum profit of ₹3200 is obtained when 8 souvenirs of type A and 20 souvenirs of type B is manufactured.

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