A firm produces 3 products `X,Y and Z` requiring minimum of three materials `A,B and C`. The per unit requirement of material are given below. Using matrix notation determine (a) Production of each product if firm has `2900,1100 and 1450` units of each material respectively. (b) Total requirement of each material if the firm produces `200,300 and 100` units of the three products respectively.

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.

A firm manufactures 3 products A,B and C.The profit are Rs.3,Rs.2 and Rs.4 respectively.The firm has 2 machines and below is the required processing time in minutes for each machine on each product:Machine M_1 and M_2 have 2000 and 2500 machine minutes respectively.The firm must manufacture 100A's,200B's and 50C's but not more than 150A's.Set up a LPP to maximize the profit.

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 firm manufactures 3 products A, B and C. the profits are Rs. 3, 2 and 4 respectively. The firm has 2 machines and below is the required processing time in minutes for each machine on each product. Machine Products A B C M_1 M_2 4 2 3 2 5 4 Machines M_1a n d\ M_2 have 2000 and 25000 machine minutes respectively. The firm must manufacture 100 As, 200B and 50Cs but not more 150 As. Set up a LPP to maximize the profit.

A factory uses three different resources for the manufacture of two different productoof the resource A, 12 units of B and 16 unit of C being available. One unit of there quires 2, 2 and 4 units of the respective resources and one unit of the second requires 4,2 and 0 units of respective resources. It is known that the first product givesatof 2 monetary units per unit and the second 3. Formulate the linear programming problem How many units of each product should be manufactured for maximizing the profit? solve it graphically.

If a firm's production department data says that the TVC for producing 8 units and 10 units of output is ₹ 2,500 and ₹ 3,000 respectively, marginal cost of 10^(th) unit will be :

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 Cutting constraints.