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One kind of cake requires 200 g of flour...

One kind of cake requires 200 g of flour and 25 g of fat and another kind of cake requires 100 g of flour and 50 g of fat. The maximum number of cakes which can be made from 5 kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes, formulate the problem as LPP.

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A company produces three types of cloth A,B and C. Three kinds of wool, say red, green and blue are required for the cloth needs 2 metres of red and 3 etres of blue wool, one unit length of type B cloth needs 3 metres of red, 2 metres of green and 2 metres of blue wool and one unit length of type C cloth needs 5 metres of green and 4 metres of blue wool. The firm has a stock of only 80 metres of red, 100 metres of green and 150 metres of blue wool. Assuming that income obtained from one unit length of cloth is ₹30, ₹50 and ₹ 40 of types . A, B and C respectively, formulate the LPP so as to maximize income.