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 x_{1} - number of hats produced by type A
Assume x_{2} - number of hats produced by type B
Maximize Z = 8x_{1} + 5x_{2}
Subject to
2x_{1} + x_{2} ≤ 500 (labour time)
x_{1} ≤ 150
x_{2} ≤ 250
x_{1}≥0, x_{2} ≥0