A firm produces two different products A and B . Each product has to undergo three operations before it takes the final shape. The profit per unit and time required per unit of each product in each operation is tabulated below:

To formulate a linear programming problem write Cutting constraints.

A firm produces two different products A and B . Each product has to undergo three operations before it takes the final shape. The profit per unit and time required per unit of each product in each operation is tabulated below: To formulate a linear programming problem write Mixing constraints.

A firm produces two different products A and B . Each product has to undergo three operations before it takes the final shape. The profit per unit and time required per unit of each product in each operation is tabulated below: To formulate a linear programming problem write Packing constraints.

A firm produces two different products A and B . Each product has to undergo three operations before it takes the final shape. The profit per unit and time required per unit of each product in each operation is tabulated below: To formulate a linear programming problem write Objective function

A manufacture produces nuts and bolts. The time required to produce one packet of nuts and one packet of bolts on machines. A and B is given the following table. He earns a profit of Rs. 25 per packet of nuts and Rs. 12 per packet of bolts. He operates his machine for atmost 15 hours a day. Formulate a linear programming problem to maximise his profit.

Following table shows a brief description about manufacturing process of a company.Time required in hours per unit of the product and maximum availability of machine is also given in the table: Write the constraints.

A firm manufactures two types of products A and B and sells them at a profit of Rs. 5 per unit of type A and Rs. 3 per unit of type B . Each product is processed on two machines M_1 and M_2 . One unit of type A requires one minute of processing time, on, M_1 and two minutes of processing time on M_2 whereas one unit of type B requires one minute of processing time on M_1 and one minute of M_2 . Machines M_1 and M_2 are respectively available for at most 5 hours and 6 hours a day. Find how many, units of each type of product should the firm produce a day, in order, to maximise the profit. Solve thè problem graphically.

A farm is engaged in breeding pigs. The pigs are fed on various products grown on the farm. To ensure certain nutrient constituents X,Y and Z, It is necessary to mix two types of feeds 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, 36 units and 100 units respectively. Product A costs Rs. 20/unit and product B costs Rs 40/unit. Formulate this problem sa a linear programming problem to minimize the total cost.

A factory produces three items P,Q and R at two plants A and B . The number of items produced and operating costs per hour is as follows: It is desired to produce at least 500 items of type P , at least 400 items of type Q and 300 items of type R per day. Write the objective function and constraints.

A diet is to contain atleast 80 units of vitamin A and 100 units of minerals.Two foods F1 and F2 are available.Food F1 costs Rs 4 per unit food and F2 costs Rs 6 per unit.One unit of food F1 contains 3 units of vitamin A and 4 units of minerals.One unit of food F2 contains 6 unit of of vitamin A and 3 units of minerals.Formulate this as a linear programming problem.Find the minimum costs for diet that consists of misture of these two foods and also meets the minimal nutritional requirements.

A firm deals with two kinds of fruit juices-pineapple and the, orange juice. These are mixed and two types of mixtures are obtained which is sold as soft drinks A and B , One tin of A need 4 litres of pineapple juice and 1 litre of orange juice. One tin of B needs 2 litres of pineapple and 3 litres of oranges juice. The firm has only 46 litres of pineapple juice and 24 litres of orange jụice. Each tin of A and B is sold at a profit of Rs. 4 /- and Rs. 3 /-respectively. How many tins of A and B should the firm produce to maximise profiț? Formulate the linear programming problem and solve it graphically.