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A firm produces two types of cloth, printed and plain. Three kinds of yarns are required to produce the cloth – red, green and blue. One unit length of printed cloth needs 2 metres of red yarn, 6 metres of blue yarn and 4 metres of green yarn. One unit length of plain cloth needs 5 metres red yarn. The firm has a stock of 8 metres of red yarn, 10 metres of green yarn and 15 metres of blue yarn. It is assumed that income obtained from one length of printed cloth is Rs. 10 and one length of plain cloth is Rs. 6. Formulate the L.P.P. so as to maximise the income obtained from the sale of finished product.

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The L.P.P. is : 

maximize Z = 10x + 6y 

Subject to constraints : 2x + 5y ≤ 8 

6x ≤ 10 

4x ≤ 15 

and x ≥ 0, y ≥ 0.

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