A company manufactures 2 kinds of hats. Each hat of the I type needs twice as much as labour time as the II type. The company can manufacture a sum of 500 hats a day. The market restricts daily sales of I and II types to 150 and 250 hats. Supposing that the gain per hat is Rs.8 for type A and Rs. 5 for type B. Develop LPP models so as to find out the number of hats to be manufactured of each type so as to maximize the gain (profit).

Answer

Assume x₁ - number of hats produced by type A

Assume x₂ - number of hats produced by type B

Maximize Z = 8x₁ + 5x₂

Subject to

2x₁ + x₂ ≤ 500 (labour time)

                        x₁ ≤ 150

                        x₂ ≤ 250

                 x₁≥0, x₂ ≥0