CUET · MATHS · PYQ PAPER 2023
A manufacturer has 3 machines I, II and III installed in his factory. Machines I and II are capable of being operated for at most 12 hrs whereas machine III is capable to operate at least 5 hrs a day. He produced only two items M and N each requiring the use of all 3 machines. Number of hours for producing 1 unit of M and N each on the 3 machines are given below:
Items No. of hours in each machine
| I | II | III | |
| M | 1 | 2 | 1 |
| N | 2 | 1 | 1.25 |
(A) Z = 600x + 400y
(B) \(x+2 y \geq 12\)
(C) \(x+\frac{5}{4} y \leq 5\)
(D) \(2 x+y \leq 12\)
- A B, C and D only
- B A and B only
- C A and D only
- D C and D only
Answer & Solution
Correct Answer
(C) A and D only
Step-by-step Solution
Detailed explanation
Let \(x\) be the number of M items and \(y\) be the number of N items. Objective Function (Profit): Profit \(Z = 600x + 400y\) This matches option (A). Constraints: Machine I (at most 12 hrs): \(1x + 2y \leq 12\) Option (B) is \(x+2 y \geq 12\), which is incorrect. Machine II…
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