A manufacture produces two products A and B. Both the products are processed on two different machines. The available capacity of first machine is 12 hours and that of second machine is 9 hours for day. Each unit of product A requires 3 hours on both machines and each unit of product B requires 2 hours on first machine and 1 hour on second machine, Each unit of product A is sold at Rs. 7 profit and  that of B at a profit of Rs. 4. Find the production level per day for maximum profit graphically.

A manufacturer produces nuts and bolts. It takes 2 hours work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 2 hours on machine B to produce a package of bolts. He earns a profit of Rs. 24 per package on nuts and Rs. 18 per package on bolts. How many packages of each should be produced each day so as to maximize his profit, if he operates his machines both for at the most 10 hours a days. Make an LPP from above and solve it graphically?

Find graphically, the maximum value of Z = 2x + 5y, subject to constraints given below: 2x + 4y \(\le \) 8 \(\Rightarrow\) x + 2y \(\le \) 4
3x + y \(\le \) 6
x + y \(\le \) 4
x \(\\ \ge \) 0, y  \(\\ \ge \) 0

A company manufactures two types of sweaters, type A and B. It costs Rs. 360 to make one unit of type A and Rs. 120 to make a unit of type B. The company can make at most 300 sweaters and can spend Rs. 72,000 a day. The number of sweaters of type A cannot exceed the number of type B by more than 100. The company makes a profit of Rs 200 on each unit of type A. The company charging a nominal profit of Rs. 20 on a unit of type B. Using LPP, solve for max. profit.

A decorative item dealer deals in two items A and B. He has Rs. 15,000 to invest and a space to store at the most 80 pieces. Item A cost him Rs. 300 and item B costs him Rs 150. He can sell items A and B at respective profits of Rs. 50 and Rs. 28. Assuming he can sell all he buys, formulate the linear programming problem in order to maximize his profit and solve it graphically.

A dietician wishes to mix two types of foods in such a way that the vitamin contents of the mixture contains at least 8 units of vitamin A and 10 units of vitamin C. Food I contains 2 units/kg of vitamin A and 1 unit/kg o6f vitamin C while food II contains 1 unit/kg of vitamin A and 2 units/kg of vitamin C. It costs Rs. 5 per kg to purchase food I and Rs. 7 per kg to purchase food II. Determine the minimum cost for such a mixture. Formulate the above as a LPP and solve it graphically.

A retired person wants to invest an amount of Rs. 50,000. His broker recommends investing in two type of bonds 'A' and 'B' yielding 10% and 9% return respectively on the invested amount. He decides to invest at least Rs. 20,000 in bond 'A'  and at least Rs. 10,000 in bond 'B'. He also wants invest at least as much in boud 'A' as in bond ·'B'. Solve this linear programming problem graphically to maximise his returns.

A housewife wishes to mix together two kinds of food X and Y, in such a way that the mixture contains at least 10 units of vitamin A, 12 units of vitamin Band 8 units of vitamin C. The vitamin contents of one kg of food is given below:

One kg of food X costs Rs. 6 and one kg of food y costs Rs. 10. Formulate the above problem as a linear programming problem and find the least cost of the mixture which will produce the diet graphically. What value will you like to attach with this problem?

A company produces soft drinks that has a contract which requires that a minimum of 80 units of the chemical A and 60 units of the chemical B go into each bottle of the drink. The chemicals are available in prepared mix packets from two different suppliers. Supplier 5 had a packet of mix of 4 units of A and 2 units of B that costs ~ 10. The supplier T has a packet of mix of 1 unit of A and 1 unit of B that costs ~ 4. How many packets of mixes from 5 and T should the company purchase to honour the contract requirement and yet maintain the minimum cost? Make a LPP and solve graphically.

A factory makes two types of items A and B, made of plywood. One piece of item A requires 5 minutes for cutting and 10 minutes for assembling. One piece of item B requires 8 minutes for cutting and 8 minutes for assembling. There are 3 hours and 20 minutes available for cutting and 4 hours for assembling. The profit on one piece of item A is Rs. 5 and that on item B is Rs. 6. How many pieces of each type should the factory make so as to maximize profit? Make it as an LPP and solve it graphically.