Ex 12.2, 7

Transcript

Ex 12.2, 7 A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A require 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. There are 3 hours 20 minutes available for cutting and 4 hours for assembling. The profit is Rs 5 each for type A and Rs 6 each for type B souvenirs. How many souvenirs of each type should the company manufacture in order to maximise the profit? According to Question As, we need to maximize the profit, so the function used here will be Maximize z. Profit on Type A → Rs. 5 Profit on Type B → Rs. 6 ∴ Maximize z = 5x + 6y Combining all Constraints : Maximize Z = 5x + 6y Subject to Constraints : 5x + 8y ≥ 200 10x + 8y ≤ 240 x ≥ 0 , y ≥ 0 Hence, Profit will be maximum if company Produces 8 souvenirs of type A and 20 Souvenirs of Type B Max. Profit = Rs. 160