Question:
A manufacturing company produces two items, A and B. Machine I (max 640 mins): A takes 20, B takes 15. Machine II (max 500 mins): A takes 5, B takes 8. Profit: A is Rs 25, B is Rs 18. Formulation is:
A manufacturing company produces two items, A and B. Machine I (max 640 mins): A takes 20, B takes 15. Machine II (max 500 mins): A takes 5, B takes 8. Profit: A is Rs 25, B is Rs 18. Formulation is:
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Always convert all time units to the same unit (minutes) before formulating.
Updated On: Jun 19, 2026
- Max $z=25x+18y$ s.t. $20x+15y \le 640, 5x+8y \le 500, x,y \ge 0$
- Max $z=25x+18y$ s.t. $20x+15y \le 640, 5x+8y \le 500, x,y \ge 0$
- Max $z=25x+18y$ s.t. $20x+5y \le 8, 5x+8y \le 10, x,y \ge 0$
- Max $z=25x+18y$ s.t. $4x+3y \le 128, 5x+8y \le 500, x,y \ge 0$
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The Correct Option is A
Solution and Explanation
Step 1: Concept
Let $x$ be units of A and $y$ be units of B.
Step 2: Analysis
- Profit function (Maximize): $Z = 25x + 18y$.
- Machine I constraint: $20x + 15y \le 640$ (10h 40m = 640 mins).
- Machine II constraint: $5x + 8y \le 500$ (8h 20m = 500 mins).
Step 3: Conclusion
The non-negativity constraints are $x, y \ge 0$. This matches Option (A). Final Answer: (A)
Let $x$ be units of A and $y$ be units of B.
Step 2: Analysis
- Profit function (Maximize): $Z = 25x + 18y$.
- Machine I constraint: $20x + 15y \le 640$ (10h 40m = 640 mins).
- Machine II constraint: $5x + 8y \le 500$ (8h 20m = 500 mins).
Step 3: Conclusion
The non-negativity constraints are $x, y \ge 0$. This matches Option (A). Final Answer: (A)
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