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 of 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 maximize the profit?

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Let the company manufacture x souvenirs of type A and y souvenirs of type B. Therefore, x ≥ 0 and y ≥ 0 The given information can be complied in a table as follows. Type A Type B Availability Cutting (min) 5 8 3 × 60 + 20 =200 Assembling (min) 10 8 4 ×...
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Let the company manufacture x souvenirs of type A and y souvenirs of type B. Therefore, x ≥ 0 and y ≥ 0 The given information can be complied in a table as follows. Type A Type B Availability Cutting (min) 5 8 3 × 60 + 20 =200 Assembling (min) 10 8 4 × 60 = 240 The profit on type A souvenirs is Rs 5 and on type B souvenirs is Rs 6. Therefore, the constraints are i.e., Total profit, Z = 5x + 6y The mathematical formulation of the given problem is Maximize Z = 5x + 6y … (1) subject to the constraints, … (2) … (3) x, y ≥ 0 … (4) The feasible region determined by the system of constraints is as follows. The corner points are A (24, 0), B (8, 20), and C (0, 25). The values of Z at these corner points are as follows. Corner point Z = 5x + 6y A(24, 0) 120 B(8, 20) 160 → Maximum C(0, 25) 150 The maximum value of Z is 200 at (8, 20). Thus, 8 souvenirs of type A and 20 souvenirs of type B should be produced each day to get the maximum profit of Rs 160. read less
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