Question

A manufacturer produces two types of products - A and B, which are subjected to two types of operations, viz. grinding and polishing. Each unit of product A takes 2 hours of grinding and 3 hours of polishing whereas product B takes 3 hours of grinding and 2 hours of polishing. The manufacturer has 10 grinders and 15 polishers. Each grinder operates for 12 hours/day and each polisher 10 hours/day. The profit margin per unit of A and B are Rs. 5/ - and Rs. 7/ - respectively. If the manufacturer ut

Accepted Answer

B. Total grinder hours = $10 	imes 12 = 120$. Total polisher hours = $15 	imes 10 = 150$. Grinding equation: $2x + 3y = 120$. Polishing equation: $3x + 2y = 150$. Solving simultaneously: $3(2x + 3y) - 2(3x + 2y) = 360 - 300 \implies 5y = 60 \implies y = 12$. $2x + 36 = 120 \implies 2x = 84 \implies x = 42$. Maximum Profit $= 5(42) + 7(12) = 210 + 84 = 	ext{Rs. } 294$.

Linear Programming Optimization

Explanation

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