One kind of cake requires 200 g of flour and 25 g of fat, and another kind of cake requires 100 g of flour and 50 g of fat. Find the maximum number of cakes which can be made from 5 kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes. Formulate the above as a linear programming problem and solve graphically.

(Manufacturing Problem) A small firm manufactures gold rings and chains. The total number of rings and chains manufactured per day is atmost 24. It takes 1 hour to make a ring and 30 minutes to make a chain. The maximum number of hours available per day is 16. If the profit on a ring is Rs. 300 and that on a chain is Rs. 190, find the number of rings and chains that should be manufactured per day, so as to earn the maximum profit. Make it as an LPP and solve it graphically.

A merchant plans to sell two types of personal computers-a desktop model and a portable model that will cost Rs. 25,000 and Rs. 40,000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchantshould stock to get maximum profit if he does not want to invest more than Rs.70 lakhs and his profit on the desktop model is Rs. 4,500 and on the portable model is Rs. 5,000. Make an LPP and solve it graphically.

A diet for a sick person must contain at least 4,000 units of vitamins, 50 units of minerals and 1,400 calories. Two foods X and Y are available at a cost of Rs. 4 and Rs. 3 per unit respectively. One unit of the food X contains 200 units of vitamins, 1 unit of minerals and 40 calories, whereas one unit of food Y contains 100 units of vitamins, 2 units of minerals and 40 calories. Find what combination of X and Y should be used to have least cost, satisfying the requirements?

A firm deals with two kinds of fruit juices- pineapple and orange juice. These are mixed and two mixtures are sold as soft drinks A and B. One tin of A requires 4 litres of pineapple and 1 litre of orange juice. One tin of B requires 2 litres of pineapple and 3 litres of orange juice. The firm has only 46 litres of pineapple juice and 24 litres of orange juice. Each tin of A and B are sold at a profit of Rs. 4 and Rs. 3 respectively. How many tins of each type should the firm produce to maximise the profit? Solve the problem graphically.

A man has Rs. 1,500 foor purchase of rice and wheat. A bag of rice and a bag of wheat cost Rs. 180 and Rs. 120 respectively. He has a storage capacity of 10 bags only. He earns a profit of Rs. 11 and Rs. 9 respectively per bag of rice and wheat. Formulate it as a linear programming problem and solve it graphically for maximum profit.

Suppose every gram of wheat produces 0.1 g of protein and 0.25 g of carbohydrates and corresponding values for rice are 0.05 g and 0.5 g respectively. Wheat cost Rs. 25 and rice Rs. 100 per kilogram. The minimum daily requirements of proteins and carbohydrates for an mixed in a daily diet to provide minimum daily requirements of proteins and carbohydrates at minimum cost, assuming that both wheat and rice are to be taken in a diet? What is your opinion about healthy diet? Name few ingredients necessary for a healthy diet.

(Transportation Problem) A catering agency has two kitchens to prepare food at two places A and B. From these places 'Mid-day Meal' is to be supplied to three different schools situated at P,Q,R. The monthly requirements of the schools are respectively 40, 40 and 50 food packets. A packet contains lunch for 1000 students. Preparing capacity of kitchen A and B are 60 and 70 packets per month respectively. The transportation cost per packet for the kitchen to schools is given below:

 How many packets from each kitchen should be transported to school so that the cost of transportation is minimum? Also find the minimum cost.

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 unit/ kg of vitamin A and 1 unit/kg of 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 produce Food I and Rs. 7 per kg to produce food II. Determine the minimum cost of such a mixture. Formulate the above as a LLP and solve 3 it graphically.

If a 20 year old girl drives her car at 25 km/h, she has to spend Rs. 4/km on petrol. If she drives her car at 40 km/h, the petrol cost increases to Rs. 5/km. She has Rs. 200 to spend on petrol and wishes to find the maximum distance she can travel within one hour. Express the above problem as a Linear Programming Problem. Write anyone value reflected in the problem.

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 dealer in rural area wishes to purchase a number of sewing machines. He has only Rs. 5,760 to invest and has space for at most 20 items for storage. An electronic sewing machine cost him Rs. 360 and a manually operated sewing machine Rs. 240. He can sell an electronic sewing machine at a profit of Rs. 22 and a manually operated sewing machine a profit of Rs. 18. Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximize his profit? Make it as a LPP and solve it graphically.

A cottage industry manufacturers pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal 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. 25 and that from a shade is Rs. 15.Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximize his profit? Formulate an LPP and solve it graphically.

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 manufacturer produces nuts and bolts. It takes 1 hours 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 Rs. 17.50 per package of nuts and Rs. 7.00 per package of bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machine for at most 12 hours a day? Form the above as a linear programming problem 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 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.

If a young man rides his motor-cycle at 25km per hour, he had to spend Rs. 2 per km on petrol with very little pollution in the air. If he rides it at a faster speed of 40km per hour, the petrol cost increases to Rs. 5 per km and rate of pollution also increases. He has Rs. 100 to spend on petrol and wishes to find what is the maximum distance he can travel within one hour. Express this problem as an LPP. Solve it graphically to find the distance to be covered with different speeds. What value is indicated in this question?