A factory produces two product `P_1a n dP_2` . Each of the product `P_1` requires 2 hrs for moulding, 3 hrs for grinding and 4 hrs for polishing, and each of the product `P_2` requires 4 hrs for moulding, 2 hrs for grinding and 2 hrs for polishing. The factory has moulding machine available for 20 hrs, grinding machine for 24 hrs polishing machine available for 13 hrs. The profit is Rs. 5 per unit of `P_1` and Rs 3 per unit of`P_2` and the factory can sell all that it produces . Formulate the problem as a linear programming problem to maximize the profit.

A firm manufactures two products A and B. Each product is processed on two machines M_1a n dM_2 . Product A requires 4 minutes of processing time on M_1 and 8 min. on M_2 ; product B requires 4 minutes on M_1 and 4 min. on M_2 . The machine M_1 is available for not more than 8 hrs 20 min. while machine M_2 is available for 10 hrs. during any working day. The products A and B are sold at a profit of Rs. 3 and Rs. 4 respectively. Formulate the problem as a linear programming problem and find how many products of each type should be produced by the firm each day in order to get maximum profit.

A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of grinding/cutting machine and a sprayer. It takes 2 hours on the grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes one 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 maximise his profit? Make an L.P.P. and solve it graphically.

A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of grinding/cutting machine and a sprayer. It takes 2 hours on the grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes one 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 maximise his profit? Make an L.P.P. and solve it graphically.

An scooterist travels at 36 km/hr for 5 hours and at 45 km/hr for 4 hours .Find his average speed for the whole journey .

A manufacturer produces two products A and B. Both the products are processed on two different machines. The available capacity of first machine is 12 hours and that of second machine is 9 hours per day. Each unit of product A requires 3 hours on both machines and each unit of product B requires 2 hours on first machine and 1 hour on second machine. Each unit of product A is sold at Rs. 7 profit and that of B at a profit of Rs. 4. Find the production level per day for maximum profit graphically.

Classify the following measures as scalars and vector: 3 km/hr

Find the fourth proportional to : 3 hrs 12 min, 24 min, 1 m 68 cm

Convert each of the following speeds in to km /hr : 14m/sec

Convert each of the following speeds into m/sec : 90km/hr

Convert each of the following speeds in to km /hr : 35m/sec