One kind of cake requires $300 g m$ of flour and $15 g m$ of fat and another kind of cake requires $150 g m$ of flour and $30 g m$ of fat. Find the maximum number of cake which can be made from $7.5 k g$ of flour and $600 g m$ of fat, assuming that there is no shortage of the other ingredients used in making the cakes. Make it as an $L . P . P$ only.

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Solution

Consider that the number of cakes of type I is $x$ and the number of cakes of type II is $y$ .

We need to maximize $z = x + y$ .

The subject to constraints is,

$300 x + 150 y \leq 7500$

$2 x + y \leq 50$

And,

$15 x + 30 y \leq 600$

$x + 2 y \leq 40$

Such that $x, y \geq 0$

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