Two models, P and Q , of a product earn profits of ₹ 100 and ₹ 80 per piece, respectively. Production times for P and Q are 5 hours and 3 hours, respe - Mathematics MCQ Mathematics Mock Test - 4 2026 | ExamTest.live

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Two models, P and Q, of a product earn profits of ₹100 and ₹80 per piece, respectively. Production times for P and Q are 5 hours and 3 hours, respectively, while the total production time available is 150 hours. For a total batch size of 40, the objective function Z is subjected to the constraints:

Solution & Step-by-step Explanation

Let x be the number of units of P and y be the number of units of Q .Objective Function: Total Profit Z = 100 x + 80 y . We want to maximize this.Time Constraint: 5 hours for P and 3 hours for Q with a limit of 150 hours \Rightarrow 5 x + 3 y \leq 150 .Batch Size Constraint: Total units cannot exceed 40 \Rightarrow x + y \leq 40 .Non-negativity: x, y \geq 0 .These match option B.

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Two models, P and Q, of a product earn profits of ₹100 and ₹80 per piece, respectively. Production times for P and Q are 5 hours and 3 hours, respectively, while the total production time available is 150 hours. For a total batch size of 40, the objective function Z is subjected to the constraints:

Max. Z = 100 x + 80 y s.t. 5 x + 3 y \geq 150, x + y \leq 40, x, y > 0

Max. Z = 100 x + 80 y s.t. 5 x + 3 y \leq 150, x + y \leq 40, x, y \geq 0

Max. Z = 100 x + 80 y s.t. 5 x + 3 y \leq 150, x + y = 40, x, y \geq 0

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