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One cake requires $\textrm 150$ gm of flour and $\textrm 50$ gm fat, and another requires $\textrm 75$gm of flour and $\textrm 75$ gm of fat. We want to make as many cakes as possible when $\textrm 1.5$kg flour and $\textrm 0.6$ kg fat are available. How many each kind should we make?.

My Attempt: If we let $x$ and $y$ as the number of cakes of first and second kind respectively, then we need two equations to get $\textrm x$ and $\textrm y$.. But, I could not get any idea to solve further. Please help. Thanks.

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    The goal is to maximize $x+y$. The flour constraint says that $150x + 75y \le 1500$, and the fat constraint is similar. Also $x,y \ge 0$. – 2017-02-09
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    @ Theopile, Could you please elaborate a bit more. I could not understand clearly – 2017-02-09
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    If all else fails, the number of possibilities is extremely limited. Just try them! You can make $10$ of the first type, and $0$ of the second. or $9$ and $2$ for eleven in total. The answer won't be too far from there... – 2017-02-09
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    @ lulu, How do I get that? Could you please show me the calculations..? – 2017-02-09
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    Just plug in values. Let $(a,b)$ be the number of cakes of the two types you try for. if we make $(10,0)$ we use up the flour, but have a little excess fat. if we make $(9,2)$ we exactly use up both (generally a good sign that we have our max.). now try $(8,*)$. see if you can make twelve that way. Or $(7,*)$ and so on. – 2017-02-09
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    @Euler If you make $x$ of the first cakes, and each of those cakes uses $150$ grams of flour, then you are using $150x$ grams of flour in total from those cakes. Similarly, you will use $75y$ grams of flour from all the second cakes. In total, this makes $150x+75y$ grams of flour. On the other hand, you have a supply of only $1.5 kg = 1500 g$ of flour. You can't exceed your supply, so $150x + 75y \le 1500$. – 2017-02-09

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Its Linear Programming Problem question -

Let x first type of cakes and y second type of case.

Maximize $S = x + y.$

Constraints to -

$150x + 75y \le 1500$

$50x + 75y \le 600$

$x, y \ge 0$

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    @ Kanwaljit Singh, I could not understand this. Could you please explain me here at chat? :: chat.stackexchange.com/rooms/53289/keep-typing – 2017-02-09