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

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