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2.
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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3.
The marketing team of a FMCG firm can sell Y units of shampoo packets at a price of Rs (10 - y/100) each. The total cost of producing Y shampoo packets is Rs Y/10. The firm incurs an additional fixed cost of Rs. 100 in production and distribution. Assume that there are no other costs.
[1] Find the number of shampoo packets that the firm should sell to maximize its profits?
(A) 495
(B) 595
(C) 450
(D) 550[2] If the fixed cost of production and distribution increases from Rs. 100 to Rs. 200, the optimal number of the shampoo packets to be sold will
(A) increase
(B) decrease
(C) not change
(D) cannot sayasked in JMET
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4.
A project requires an initial capital investment of Rs. 2 lakhs which yields a onetime benefit at the end of the second year.
[1] If the cost of capital is 10%, what should be the minimum yield that would justify an investment in this project?
(1) Rs. 2,42,000
(2) Rs. 2,40,000
(3) Rs. 2,20,000
(4) Rs. 2,22,000[2] Suppose the investment of Rs. 2 lakhs in the above project can be made in two equal instalments of Rs. 1 lakh in the beginning of the project and the other Rs. 1 Lakh at the beginning of the second year. From the beginning of the third year, the project will generate revenues of Rs. 1.5 lakhs every year. Using the same cost of capital of 10%, what should be the minimum life of the project inclusive of the project implementation phase? (Use the 'beginning of the year' convention)
(1) 3 years
(2) 5 years
(3) 4 years
(4) 6 yearsasked in JMET
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