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:

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

{\x}

and

{\y}

, respectively. To maximize :

{\Z}=₹(100 {\x}+120 {\y})

Subject to constraints :

x ≥ 0

y ≥ 0

5 x+8 y ≤ 200

10 x+8 y ≤ 240

Corner Points	Value of $\bo {Z}$ (in ₹)
${\A}(0,25)$	3000
${\B}(8,20)$	$3200 ←$ 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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