George wants your help to work out how many of each type he should stock in order to maximise his profit. There are three types of Snackboxes: A, B and C. A and C both cost 5 to produce, and B cost 7 to produce. He sells A to the students for 15 each, B for 23 each, and C for 7 each. George knows that he can only order up to 200 Skiving Snackboxes in total, and he must order at least 14 of each type. The number of C ordered must be less than or equal to half the number of A and B combined.
George is now required to ensure that the cost of the ordered C must make up at least 15% of the total cost of the Snackboxes ordered. Show how you would enforce this extra requirement in your linear program.
Ok, now I've finally read the problem which is a linear optimization one:
$$\begin{align*}\text{Cost function: }&\;\;f(A,B,C)=\;\;5A+7B+5C\\ \text{Profit function:}&\;\;P(A,B,C)=15A+23B+7C\end{align*}$$
with the constraints:
$$A+B+C\le200\;,\;\;A,B,C\ge14\;,\;\;C\le\frac12(A+B)\;,\;\;f(A,B,C)\le(0.15)5C=\frac34C$$
And thus, when you find the minimum of $\,f\,$/maximum of $\,g\,$ evaluating on the constraints domain's vertices, you'll have to make sure of the last constraint above, i.e. $\;f\le\frac34C\;$ , which could mean you'll have to take some other point(s) of on the domain of the one you already had...