use a linear programming model to identify the optimal product mix using the following data:

Product Raw material$($kg$)$ Machine capacity$($min$)$ Labor capacity$($min$)$ Maximum average demand Profit of a unit $($$$)$

A $0\mathrm{.}250\mathrm{.}350\mathrm{.}831300004$

B $0\mathrm{.}050\mathrm{.}550\mathrm{.}60750003$

C $0\mathrm{.}170\mathrm{.}230\mathrm{.}79250006$

D $0\mathrm{.}070\mathrm{.}791\mathrm{.}31600012$

E $0\mathrm{.}110\mathrm{.}140\mathrm{.}381400002$

The monthly available tea leaf $($the raw material of the tea$)$ is $35000$ kilograms

The maximum capacity of the $7$ lines is $250,000$ box$/$month$.$

why arent we using the maximum profit numbers as the base of calculation for the Z and instead you used the avergage maximum demand numbers? so why did you use: maximize z: $13000$xa $...$and not maximize z: $4$xa$?$