algebra question

Question

An aircraft factory manufactures airplane engines. The unit cost C(the cost in dollars to make each airplane engine) depends on the number of engines made. If x engines are made, then the unit cost is given by the function C(x)=0.1^2x22x+8292. How many engines must be made to minimize the unit cost?

Do not round your answer.

Answer 1

If it reads

C(x) = -.1x^2 +22x + 8292

then

C'(x) = -.2x +22 = 0

x = 22/.2 = 110 engines to minimize per unit cost

but it's unclear what ".1x22x" means. so anything is possible

But the basic optimization method is

take the derivative of cost and set it equal to zero then solve for x

to find the cost minimizing output level

this problem probably would be more appropriate under the categories of

calculus, derivatives or microeconomics