A plumber can be paid under two schemes as given below : (I) : Rs. 600 and Rs. 50 per hour (II) : Rs. 170 per hour. If the job takes n hours, for what value of n does the scheme I give the plumber the better wages.

A manufacturer has three machines I, II and III installed in his factory. Machines I and II are capable of being operated for at most 12 hours whereas machine III must be operated for at least 5 hours a day. She produces only two items M and N each on the three machines are given in the following table: SHe makes a profit of Rs 600 and Rs 400 on items M and N respectively. How many of each item should she produce so as to maximise her profit assuming that she can sell all the items that she produced? What will be the maximum Profit?

A soft drinks manufacturing company is preparing a production plan on two types A and B of soft drinks. There is sufficinet materail available to make 20000 bottles of drink A and 40000 bottles of drink B but there are only 45000 empty bottles into either hte drinks can be filled. Further, it takes 3 hours to fill 1000 bottles of drink A and one hour to fill 1000 bottles of drink B. there are only 66 hours available for filling. The profit is Rs.2 per bottle for drink A and Rs.1 per bottle of drink B. Set up this problem as a linear programming problem and find graphically the production scheduled in order to maximize the profit.

A manufacture produces two Models of bikes. Model X and Model Y. Model X takes a 6 man hours to make per unit, while Model Y takes 10 man hours per unit. There is a total of 450 man hour available per week handing and marketing costs are Rs.2000 and Rs.1000 per unit of MOdels X and Y respectively. the total funds avilable for these purposes are Rs.80000 per week. Profits per units for Models X and Y are Rs.1000 and Rs.500 respectively. how many bikes of each model should be the manufacture producer so as to yield a maximum profit? find the profit.

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 machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs17.50 per package on nuts and Rs 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours a day?

A man rides his motorcylcle at the speed of 50 km/hour. He has to spend Rs.2 per km on petrol. If the rides it as a faster speed of 80 km/hour, the petrol cost increases to Rs.3 per km. he has atmost Rs.120 to spend on petrol and one hour's time, He wishes to find the maximum distance that he can travel Express this problem as a linear programming problem and solve it graphically to find the maximum distance he can travel.

A manufacturing company makes two types of teaching aids A and B of Maths for class XII. Each type of A requires 9 labour hours for fabricating and 1 labour hour for fininshing. Each type of B requires 12 labour hours for fabricating and 3 labour hours for fininshing. For fabricating and finishing , the maximum labour hours available are 180 and 30 respectively. The company makes a profit of Rs 80 and each type of A and Rs 120 on each type of B. How many pieces of type A and type B should be manufactured per week to realise a maximum profit? What is the maximium profit per week?

A manufacturer of patent medicines is preparing a production plan on medicines, A and B. There are sufficient raw materials available to make 20000 bottles of A and 40000 bottles of B, but there are only 45000 bottles into which either of the medicines can be put. Further, it takes 3 hours to prepare enough material to fill 1000 bottles of A, it takes 1 hour to prepare enough material to fill 1000 bottles of B and there are 66 hours available for this operation. The profit is Rs 8 per bottle for A and Rs 7 per bottle for B. How should the manufacturer schedule his production in order to maximize his profit?

A manufacturer makes two types of toys A and B. Three machines are needed for this pupose and the time (in minutes ) required for each toy on the machines is given below : Each machine is available for a maximum of 6 hours per day. If the profit on ech toy of type A is Rs 7.50 and that on each toy B is Rs 5, show that 15 toys of type A and 30 of type B should be manufactured in a day to gat maximum profit.

A manufacture make two types of toys A and B. three machines are needed for this purpose and the time required for each toy on the machines is given below: Each machine is available for a maximum of 6 hours per day. if hte profit on each type A is Rs.7.50 and that on each toy of type B is Rs.5. show that 15 toys of type A and 30 of type B should be manufactured in a day to get maximum profit.