Question 250495
First we have a profit function as:
{{{P = 25D + 30S}}}
Second, we have D >= 80 and S >= 100. graph those on a coordinate system where D is x-axis and S is y-axis.
Third, we have D + S <= 200. Graph that on a coordinate system. Notice we get a "feasible region" which looks like a small triangle. We want the coordinates of the three verticies. They are: (80, 100) ; (80,120) ; (100,100).
Put these into the profit function and we get,
{{{P = 25*80 + 30*100}}} - -> P = 5000
{{{P = 25*80 + 30*120}}} - -> P = 5600
{{{P = 25*100 + 30*100}}} - -> P = 5500.

WE can see max profit at (80, 120).
we need to produce 80 deluxe and 120 standard.