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Manufacturing of two automotive gear products. A and B. requires processing in both machines 1 And 2. The time required to manufacture one unit of Product A, on machine 1 and machine 2 are 2 hours and 4 hours respectively. Whereas, the time required for manufacturing one unit of Product B on machine 1 and machine 2, are 3 hours and 1 hour respectively. The total time available for machine 1 and machine 2 on a given working day are 6 hours and 8 hours respectively. There is also a constraint that at least 8 units of A and B together should be produced in a given day. Per unit profit of A and B are Rs. 5 and Rs. 7 respectively. The objective is to maximize the total amount of profit by manufacturing the two products on any given day.
[1] If X and Y represent the number of A and B to be produced on a given day respectively, then the mathematical formulation for the daily profit maximization problem is given by:
1). Max profit = 5X + 7Y
2X + 3Y ≤ 6
4X + Y ≤ 8
X + Y ≥ 8
X, Y ≥ 0 and integers
2). Max profit= 5X + 7Y
6X + 8Y ≤ 2
4X + Y ≤ 3
X + Y ≥ 8
X, Y ≥ 0 and integers
3). Max profit = 5X + 7y
2X + 4Y ≤ 6
3X + Y ≥ 8
X + Y ≥ 8
X, Y ≥ 0 and integers
4). Max profit = 5X + 7Y
2X + 3Y ≤ 6
4X + Y≤ 8
X + Y ≤ 8
X, Y ≥ 0 and integers
[2] The values of (X, Y) at which optimality is reached is:
(1) (0, 8)
(2) (8, 0)
(3) Infeasible
(4) Infinite
asked in JMET
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