### 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
In Corner point method for solving a linear programming problem the first step is to
1. Find the infeasible regions of the linear programming problem and determine theunion of the infeasible regions
2. Find the infeasible region of the linear programming problem and determine its complement
3. Find the feasible region of the linear programming problem and determine its center points (vertices).
4. Find the feasible region of the linear programming problem and determine its corner points (vertices)
Corner points of the feasible region for an LPP are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5).Let F = 4x + 6y be the objective function. Maximum of F – Minimum of F =
1. 60
2. 42
3. 18
4. 48
In linear programming infeasible solutions
1. fall inside the a regular polygon
2. fall inside the feasible region
3. fall on the x = 0 plane
4. fall outside the feasible region
A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours. The profit from the sale of a lamp is Rs 5 and that from a shade is Rs 3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximize his profit?
1. 4 Pedestal lamps and 5 wooden shades; Maximum profit = Rs 36
2. 5 Pedestal lamps and 5 wooden shades; Maximum profit = Rs 38
3. 5 Pedestal lamps and 4 wooden shades; Maximum profit = Rs 35
4. 4 Pedestal lamps and 4 wooden shades; Maximum profit = Rs 32
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