Two tailors A and B earn Rs. 150 and Rs. 200 per day respectively. A can stitch 6 shirts and 4 pants per day while B can stitch 10 shirts and 4 pants per day. Form a linear programming problem  to minimize the labour cost to produce at least 60 shirts an 32 pants.

Two tailors A and B earn Rs. 150 and Rs. 200 per day respectively. A can stich 6 shirts and 4 pants per day, while B can stitch 10 shirts and 4 pants per day. Form a L.P .P to minimize the labour cost to produce (stitch) at least 60 shirts and 32 pants and solve it graphically.

Two tailors, A and B, earn 300 and 400 per day respectively. A can stitch 6 shirts and 4 pairs of trousers while B can stitch 10 shirts and 4 pairs of trousers per day. To find how many days should each of them work and if it is desired to produce at least 60 shirts and 32 pairs of trousers at a minimum labour cost, formulate this as an LPP.

Two tailors A and B earns 15 and 20 per dayrespectively. A can stitch 6 shirts and 4 paints while Bcan stitch 10 shirts and 4 paints per day. To minimise the cost to stitch 60 shirts and 32 paints, how manydays should they work?

Manufacturer produces two types of steel trunks. He has two machines, A and B. The first type of trunk requires 3 hours on machine A and 3 hours on machine B. The second type requires 3 hours on machine A and 2 hours on machine B. Machines A and B can work at most for 18 hours and 15 hours per day respectively. He earns a profit of Rs. 30 per trunk on the first type of trunk and Rs. 25 per trunk on the second type. Formulate a linear programming problem to find out how many trunks of each type he must make each day to maximize his profit.

A farm is engaged in breeding pigs. The pigs are fed on various products grown on the farm. In view of the need to ensure certain nutrient constituents (call them X,Y and Z), it is necessary to buy two additional products, say, A and B. One unit of product A contains 36 units of X, 3 units of Y, and 20 units of Z. One unit of product B contains 6 units of X, 12 units of Y and 10 units of Z. The minimum requirement of X, Y and Z is 108 units respectively. Product A costs LRs. 20 per unit and product B costs Rs. 40 per unit. Formulate the above as a linear programming problem to minimize the total cost, and solve the problem by using graphical method.

A oil company requires 12000, 20000 and 15000 barrels of high grade, medium grade and low grade oil respectively. Refinery A produces 100, 300 and 200 barrels per day of high, medium and low grade oil respectively whereas the refinery B produces 200, 400 and 100 barrels per day respectively. If A costs 400 per day and B cost 300 per day to operate. To find how many days should each be run to minimize the cost of requirement, formulate this as a L.P.P.

A dietician wishes to mix two types of food in such a way that the vitamin contents of the mixture contain at least 8 units f Vitamin A and 10 units of vitamin C, Food ‘I’ contains 2 units per kg of vitamin A and 1 unit per kg of vitamin C while food ‘II’ contains 1 unit per kg of vitamin A and 2 units per kg of vitamin C. It costs Rs 50.00 per kg to purchase food ‘I’ and Rs. 70.00 per kg to produce food ‘II’. Formulate the above linear programming problem to minimize the minimize the cost of such a mixture.

A company is making two products A and B. The cost of producing one unit of products A and B are Rs. 60 and 80 respectively. As per the agreement, the company has to supply at least 200 units of product B to its regular customers. One unit of product A requires one machine hour whereas product B has machine hours available abundantly within the company. Total machine hours available for product A are 400 hours. One unit of each product A and B requires one labour hour each and total of 500 labour hours are available. The company wants to minimize the cost of production by satisfying the given requirements. Formulate this problem as a LPP.

A diet is to contain at leat 80 units of vitamin A and 100 units of minerals. Two foods F_(1) and F_(2) are available. Food F_(1) cost Rs. 4 per unit and F_(2) costs Rs. 6 per unit. One unit of food F_(1) contains 3 units of vitamin A and 4 units of minerals. One unit of food F_(2) contains 6 units of vitamin A and 3 units of minerals. Formulate this as a linear programming problem. Find the minimum cost for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements.

A farm is engaged in breeding hens. The hens are fed products A and B grown in the farm which contains nutrients P, Q and R. One kilogram of product A contains 36 units, 3 units and 20 units of nutrients P Q and R respectively, whereas one kilogram of product B contains 6 units, 12 units and 10 units of nutrients P, Q and R respectively. The minimum requirement of nutrients P Q and R for a hen is 108, 36 and 100 units respectively. Product A costs 20 per kilogram and product B costs 40 per kilogram. Using linear programming, find the number of kilograms of products A and B to be produced to minimize the total cost. Identify the feasible region from the rough sketch.