A company is producing three products P₁, P₂ and P₃, with profit contribution of Rs.20, Rs.25 and Rs.15 per unit respectively. The resource requirements per unit of each of the products and total availability are given below.

Formulate the above as a linear programming model.

A soft drink company has two bottling plants C₁ and C₂. Each plant produces three different soft drinks S₁, S₂ and S₃. The production of the two plants in number of bottles per day are:

A market survey indicates that during the month of April there will be a demand for 24000 bottles of S₁, 16000 bottles of S₂ and 48000 bottles of S₃. The operating costs, per day, of running plants C₁ and C₂ are respectively Rs.600 and Rs.400. How many days should the firm run each plant in April so that the production cost is minimized while still meeting the market demand? Formulate the above as a linear programming model.

A company produces two types of products say type A and B. Profits on the two types of product are Rs.30/- and Rs.40/- per kg respectively. The data on resources required and availability of resources are given below.

Formulate this problem as a linear programming problem to maximize the profit.

Construct a network diagram for the following situation:
A < D, E; B, D < F; C < G and B < H.

A firm manufactures pills in two sizes A and B. Size A contains 2 mgs of aspirin, 5 mgs of bicarbonate and 1 mg of codeine. Size B contains 1 mg. of aspirin, 8 mgs. of bicarbonate and 6 mgs. of codeine. It is found by users that it requires atleast 12 mgs. of aspirin, 74 mgs.of bicarbonate and 24 mgs. of codeine for providing immediate relief. It is required to determine the least number of pills a patient should take to get immediate relief. Formulate the problem as a standard LLP.