A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on maching A and 1 hour on machine B to produce a package of botls. He earns a profit of Rs. 17.50 per pack age and nuts and Rs. 7.00 per pakage on bolts. How many package of each should be produced each day as to maximise his profit, if he operates his machine for at the most 12 hours a day ?

Condier the following problem. A manufacture produced tables and chairs. It takes 3 hours of work on machine A mind 1 hour of work on machine B to produce one table and 2 hours of work on machine A and 3 hours on machine B to produce 1 chair . He erars a profit fo Rs. 50 per table and Rs 40 per chair. Hoperates the machines a and B for atmost 12 hours hours respectively. how many tables and chairs should be produce each day to maximise his profit ? (i) Write the objective function. (ii) Write the constrains.

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 to manufacture a package of screws A while its 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 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 spayar. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to mafnufacture a pedstal 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 form a shade is Rs. 3 Assuming that the manufacture can sell all the lamps and shades his daily production in order to maximise his profit ?

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

A tyre manufactureing company produces tyres of cars and buses. Three machines A, B, C are to be used for the production of these typres. Machines A and C are available for operation atmost 11 hours, whereas B must be operated for atleast 6 hours a day. the time required for construction of one typre the three machines given in the following table. Comapy sells all the tyres and gets a profit of Rs. 100 Rs 150 on a tyre of a car and bus respectively. The company wants to know how many numbers of each item to be produced to maximise the profit. To formulate a linear programmining problem, (i) Write the objective function. (ii) Write all constraints.