GATE ME 2022 Set 2 — Question 42
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Industrial Engineering → Operations Research → LP (Graphical & Simplex)
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Question
A manufacturing unit produces two products P1 and P2. For each piece of P1 and P2, the table below provides quantities of materials M1, M2, and M3 required, and also the profit earned. The maximum quantity available per day for M1, M2 and M3 is also provided. The maximum possible profit per day is ₹__________.
| M1 | M2 | M3 | Profit per piece (₹) | |
|---|---|---|---|---|
| P1 | 2 | 2 | 0 | 150 |
| P2 | 3 | 1 | 2 | 100 |
| Maximum quantity available per day | 70 | 50 | 40 |
Correct answer
(B) 4000
Solution
Let and be the number of units of P1 and P2 produced per day, respectively.
Maximize
Subject to:
Maximize
Subject to:
1. (M1 constraint)
2. (M2 constraint)
3. (M3 constraint)
4.
Evaluating corner points of the feasible region:- Intersection of M1 and M2: and . Point .
- Intersection of M1 and M3: . Point .
- .
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