GATE ME 2016 Set 3 — Question 65
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Question
A firm uses a turning center, a milling center and a grinding machine to produce two parts. The table below provides the machining time required for each part and the maximum machining time available on each machine. The profit per unit on parts I and II are Rs. 40 and Rs. 100, respectively. The maximum profit per week of the firm is Rs._________
| Type of machine | Machining time required for the machine part (minutes) I | Machining time required for the machine part (minutes) II | Maximum machining time available per week (minutes) |
|---|---|---|---|
| Turning Center | 12 | 6 | 6000 |
| Milling Center | 4 | 10 | 4000 |
| Grinding Machine | 2 | 3 | 1800 |
Correct answer
39000 to 41000
Solution
Let and be the number of units of parts I and II produced per week, respectively.The objective is to maximize the total profit:
Maximize Subject to the following constraints based on machine availability:
Substituting into :
Check this point in the third constraint: (Satisfied)
At : Comparing the values, the maximum profit is Rs. 40,000, which falls within the range of 39000 to 41000.
Maximize Subject to the following constraints based on machine availability:
1.Turning Center:
2.Milling Center:
3.Grinding Machine:
4.Non-negativity:
To find the maximum profit, we evaluate the objective function at the corner points of the feasible region:- At :
- At (from ):
- At (from ):
- Intersection of and :
Substituting into :
Check this point in the third constraint: (Satisfied)
At : Comparing the values, the maximum profit is Rs. 40,000, which falls within the range of 39000 to 41000.
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