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 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 ?

A company manufactures two proudcts. A and B on which the profits erarned per unit areRs. 30 and Rs. 40 respectively. Each product is procced on two machines M_(1) and M_(2) . One unit of product A requires on hour of processing time on M_(1) and 2 hours on M_(2) While one unit of product B requires one hour each on M_(1) and M_(2) . Machines M_(1) and M_(2) are availabe atmost 10 hours and 12 hours respectivrely during working day. The company wants to know how many units of proudcts A and B should be produced to maximise the profit. to formulate a linearprogramming problem (i) Write the objective function. (ii) Write all contraints.

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.

A factory has two machines A and B. Past record shows that machine A produced 60% of the items of output and machine B produced 40% of the items. Further, 2% ol the items produced by machine A and 1% produced by machine B were defective. All the items are put into one stockpile and then one item is chosen at random from this and is found to be defective. What is the probability that it was produced by machine B: