Question $1(1$ point$)$

You are a chemical engineer engaged by Chembest Company to optimize its waste disposal situation. Chembest has a best$-$selling product $P\mathrm{.}1kg$ of $P$ requires $1kg$ of A and $2\mathrm{.}5kg$ of $B$ to make, but also results in $1kg$ of waste product $W.$

$1$kgA$+2\mathrm{.}5kgB1kgP+1kgW$

There are $3$ ways to dispose of $W$ : $($a$)$ make $1kg$ of side product $x1$ by reacting $1kg$ W with $1$kgA; $($b$)$ make $1kg$ of side product X$2$ by reacting $1kg$ W with $1kgB$; $($c$)$ chemically treat $W$ to make it harmless.

$P$ and $x2$ bring in revenues of $$\frac{2500}{k}g$ and $$\frac{200}{k}g$ respectively. Each $kg$ of $x1$ produced costs the company $$50.$ The chemical treatment costs $$\frac{300}{k}g$ W$.$ Furthermore, only $7500$ kg A and $10000$ kg B are available.

What is the maximum profit the company can make $($Profit $=$ Total revenue $-$ Total cost$)?$ Give your answer to the nearest whole number. $($Please help to provide details working! Thank you$)$

$7500$kg of P produced required $18750$kg of B according to the equation above A $+2\mathrm{.}5$B$=$P $+$ W