A firm can produce three types of cloth say 'A', 'B' and 'C'.Three kinds of wool are required for it, say red wool, green wool and blue wool.One unit length of type 'A' cloth needs 2 yards of red wool and 3 yards of blue wool, one unit length of type 'B' cloth needs 3 yards of red wool, 2 yards of gren wool and 2 yards of blue wool, one unit length of type 'C' cloth needs 5 yards of green wool and 4 yards of blue wool.The firm has only a stock of 8 yards of red wool, 10 yards of green wool and 15 yards of blue wool.It is assumed that the income obtained from one unit of type 'A' cloth is ₹ 3, for type 'B' cloth is ₹ 5 and for type 'C' cloth is ₹ 4.Formulate the problem as a LPP so as to maximize the profit of the firm by using the available materials.

Answer

Maximize `P = 3x + 5y + 4z` subject to:
`2x + 3y le 8, 2y+ 5z le 10, 2y + 4z le 15, x ge 0, y ge 0, z ge 0`.