Question

A chemical manufacturer sells sulfuric acid in bulk at a price of $100 per unit. If the daily production cost in dollars for x units is: C(x)=100,000+50x+0.0025x^2, and if the daily production capacity is at most 7000 units, how many units of sulfuric acid must be manufactured and sold daily to maximize the profit?

Answer 1

For the given information, you have two different functions: on for cost C(x) and one for income F(x)=100x Profit is when you subtract cost from income so if you do that with the two functions that you have, you get
P(x)=F(x)-C(x)
P(x)=100x-0.0025x^2-50x-100000
P(x)=-0.0025x^2+50x-100000 <<< This is function for profit
If you graph P(x), you can see that profit is maximized at 7000 units

Answer 2

*one

Answer 3

This is sort of what the graphs look like. C(x) and F(x) intersect closer to x=0 and C(x) is very slightly curved