Math Help - Linear programming question

1. Linear programming question

DuPhos produces two chemicals: Formula S and Formula T.

14. Re: Linear programming question

Thanks for your help but I still have no idea.

I'll put this one in the too hard basket for now and come back to it when I practise these a bit more.

Thanks again for your attempts at helping this lost soul!

Lance

15. Re: Linear programming question

$\\x_1:\mbox{units of process 1}\\x_2:\mbox{units of process 2}\\x_3:\mbox{grams of Formula S produced}\\x_4:\mbox{grams of Formula T produced}\\x_5:\mbox{grams of Formula T to be disposed}\\ \\ \mbox{Labor amount: } 2x_1+3x_2 \leq 60 \\ \mbox{Material amount: } 500x_1+1000x_2 \leq 20000 \\ \\ \mbox{Formula S produced: } x_3=50x_1+75x_2\\ \mbox{Formula T produced: } x_4=25x_1+50x_2 \\ \mbox{Formula T to be disposed: } x_5 =\begin{cases}0 & x_4 \leq 500\\x_4-500 & x_4 > 500\end{cases} \\ \mbox{Revenue: } Z=16x_3+14x_4-16x_5$
$2x_5$ from disposal plus $14x_5$ (cost of opportunity, i.e loss of what we could sell from formula T if we could sell more than 500 grams). As we have consider sales of all formula T in the revenue formula we have to subtract cost of opportunity from the revenue.