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$.$

so based on changing the Z condition to the maximum profit and not demand, do the rest of the equations and product mix provided earlier still apply? using the first three products at keeping the last two products at zero?