### Class XII

A factory manufactures two types of screws, A and B. Each type of screw requires the use of two machines, an automatic and a hand operated. It takes 4 minutes on the automatic and 6 minutes on hand operated machines tomanufacture a package of screws A, while it takes 6 minutes on automatic and 3 minutes on the hand operated machines to manufacture a package of screws B. Each machine is available for at the most 4 hours on any day. The manufacturer can sell a package of screws A at a profit of Rs 7 and screws B at a profit of Rs 10. Assuming that he can sell all the screws he manufactures, how many packages of each type should the factory owner produce in a day in order to maximize his profit? Determine the maximum profit
1. 30 packages of screws A and 22 packages of screws B; Maximum profit = Rs 412
2. 32 packages of screws A and 22 packages of screws B; Maximum profit = Rs 414
3. 30 packages of screws A and 20 packages of screws B; Maximum profit = Rs 410
4. 32 packages of screws A and 20 packages of screws B; Maximum profit = Rs 412
Let R be the feasible region for a linear programming problem, and let Z = ax + by be the objective function. If R is bounded, then
1. the objective function Z has both a maximum and a minimum value on R
2. the objective function Z has only a maximum value on R
3. the objective function Z has no minimum value on R
4. the objective function Z has only a minimum value on R
There are two types of fertilizers F1 and F2. F1 consists of 10% nitrogen and 6% phosphoric acid and F2 consists of 5% nitrogen and 10% phosphoric acid. After testing the soil conditions, a farmer finds that she needs atleast 14 kg of nitrogen and 14 kg of phosphoric acid for her crop. If F1 costs Rs 6/kg and F2 costsRs 5/kg, determine how much of each type of fertiliser should be used so that nutrient requirements are met at a minimum cost. What is the minimum cost?
1. 120 kg of fertilizer F1 and 80 kg of fertilizer F2; Minimum cost = Rs 1200
2. 130 kg of fertilizer F1 and 80 kg of fertilizer F2; Minimum cost = Rs 1300
3. 110 kg of fertilizer F1 and 80 kg of fertilizer F2; Minimum cost = Rs 1100
4. 100 kg of fertilizer F1 and 80 kg of fertilizer F2; Minimum cost = Rs 1000
Minimize Z = 50x+60y , subject to constraints x +2 y ≤ 50 , x + y ≥ 30, x, y ≥ 0.
1. 1200
2. 1550
3. 1700
4. 1800
Maximize Z = 3x + 4y, subject to the constraints: x + y ≤ 1, x ≥ 0, y ≥ 0.
1. 5
2. 3
3. 4
4. 6
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