(Manufacturing problem) A manufacturing company makes two models A and B of a product. Each piece of Model A requires 9 labour hours for fabricating and 1 labour hour for finishing. Each piece of Model B requires 12 labour hours for fabricating a

A manufacturing company makes two modeis A and B of a product. Each piece of model A requires 9 labour hours for fabricating and 1 labour hour for finishing. Fach piece of model B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available are 180 and 30 respectively. The company makes a profit of Rs. 8,000 on each piece of modal A and Rs. 12,000 on week maximum profit ? What is the maximum profit per week ?

A Company manufactures two types of novelty sovenirs made of plywood . Souvenirs of type A require 5 min each for cutting and 10 min each for assembling . Souvenirs of type B require 8 min each for cutting and 8 min each for assembling . There are 3 h 20 min available for cutting and 4 h for assembling . The profit is Rs 5 each for type A and Rs 6 each for type B souvenirs . How many souvenir of each type should the company manufacture in order to maximise the profit ?

A factor 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 to maufacture a package of screw s A, while it take 6 minutes on automatic and 3 minutes on the hand operated machines to maufacture 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 screw he manufactures, how many packages of each type should the factory owner produced day in order to maximise his profit? Determine the maximum profit.

A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding cutting machine and a sprayer . It takes 2 h on grinding cutting machine and 3 h on the sprayer to manufacture a pedestal lamp . It takes 1 h on the grinding cutting machine and 2 h on the sprayer to manufacture a shade . On any day, the sprayer is available for at the most 20 h and the grinding cutting machine for at the most 12 h . The profit from the sale of a lamp is Rs 5 and that from a shade is Rs 3 . Assuming that the manufacture can sell all the lamps and should he schedule his daily production in order to miximize his profit ?

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method : Places A and B are 100 km apart on highway. One car starts from A and another form B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars ?

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method : Places A and B are 100 km apart on a highway. One car starts from A and another from B at same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars ?

Form the pair of linear equations in the following problems and their solutions (if they exist) by any algebraic method. Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?

Carry out the following osmosis experi ment. Take four peeled potato to halves and scoop each one out to make potato cups one of these potato cups should be made from a boiled potato. Put each potato cup in a tray containing water . Now (a) Keep cup A empty (b) Put one teaspoon sugar in cup B ( c) Put one teaspoon sugar in the boiled potato cup D. Keep these for two hours . The observe the four potato cups and answer the following : M (i) Explain why water gathers in the hollowed portion of B and C . (ii) Why is potato A necessary for the experiment . (iii) Explain why water does not gather in the hollowed out portions of A and D.

(a) Determine the electrostatic potential energy of a system consisting of two charges 7 µC and –2 µC (and with no external field) placed at (–9 cm, 0, 0) and (9 cm, 0, 0) respectively. (b) How much work is required to separate the two charges infinitely away from each other? (c) Suppose that the same system of charges is now placed in an external electric field E = A(1//r^(2)):A = 9 xx 10^(5) NC^(-1) . What would the electrostatic energy of the configuration be?