A manufacturer produces nuts and bolts . It takes 1 hr of work on machine A and 3 hr on machine B to produce a package of nuts and bolts . He earns a profit of Rs 17.50 per package on nuts and Rs 7.00 per package on bolts . How many package of each should be produced each most 12 h a day to maximize 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 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 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 ?

A factory makes tennis rackets and cricket bats . A tennis racket takes 1.5 h of machine time and 3 h of craftman's time in its making while a cricket bat takes 3 h of machine time and 1 h of craftman' time . In a day , the factory has the availability of not more than 42 h of machine time and 24 h of craftman's time (a) What number of rackets and bats must be made, if the factory is to work at full capacity? (b) If the profits on rackets and on bats is Rs 20 and Rs 10 respectively , find the maximum profit of the factory when it works at full capacity .

A manufacturer considers that men and women workers are equally efficient and so he pays them at the same rate. He has 30 and 17 units of workers male and female and capital respectively, which he uses to produce two types of goods A and B. To produce one unit of A, 2 workers and 3 units of capital are required while 3 workers and 1 unit of capitals required to produce one unit of B. If A and Bare priced at 100 rupeya and 120 rupeya per unit respectively,how should he use his resources to maximize the total revenue ? Form the above as an LPP and solve it graphically .

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 manufacturer produces three products x, y, z which he sells in two markets. Annual sales are indicated below: {:("Market",,"Products",),(I,"10,000","2,000","18,000"),(II,"6,000","20,000","8,000"):} (a) If unit sale prices of x, y and z are Rs. 2.50, Rs. 1.50 and Rs. 1.00, respectively, find the total revenue in each market with the help of matrix algebra. (b) If the unit costs of the above three commodities are Rs. 2.00, Rs. 1.00 and 50 paise respectively. Find the gross profit.