GATE ME 2017 Set 1 — Question 51
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Industrial Engineering → Operations Research → LP (Graphical & Simplex)
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Question
Two models, P and Q, of a product earn profits of Rs. 100 and Rs. 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, to maximize profit, the number of units of P to be produced is ________.
Correct answer
15 to 15
Solution
Let be the number of units of model P and be the number of units of model Q.
Objective function: Maximize
Constraints:
1) (Time constraint)
2) (Batch size constraint)
3) From (2), . Substitute this into (1):
Substitute into the profit function:
To maximize , we must maximize . The maximum value of is 15.
Objective function: Maximize
Constraints:
1) (Time constraint)
2) (Batch size constraint)
3) From (2), . Substitute this into (1):
Substitute into the profit function:
To maximize , we must maximize . The maximum value of is 15.
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