A firm can produce three types of cloth say `C_1,C_2,C_3` . Three kinds of wool are required for it, say red wool, green wool and blue wool. One unit of length `C_1` needs 2 metres of red wool, 3 metres of blue wool; one unit of cloth `C_2` needs 3 metres of red wool 2 metres of blue wool and 2 metres of green and one unit of cloth `C_3` needs 5 metres of green wool and 4 metres of blue wool. The firm has only a stock of 16 metres of red wool, 20 metres of green wool and 30 metres of blue wool. It is assumed that the income obtained from one unit of length of cloth `C_1` is Rs. 6, of cloth `C_2` is Rs. 10 and of cloth `C_3` is Rs. 8. Formulate the problem as a linear programming problem to maximize the income.