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?

to solve the amount of sulfuric acid to maximize the profit we need to establish the profit

let S (x) = 100x the selling price

P = S (x) - C (x)

P = 100x - (100,000 + 50x + 0.0025x^2)

P = 50x - 100000 - 0.0025x^2

Getting the first derivative and equating it to 0

0 = 50 - 0.005x

X = 10000 units of sulfuric acid

But the capacity is only 7000 units

So 7000 units should be manufactured