Polynomial Optimization Applications questions, I don't know how to find the answers. thanks?

Question

Polynomial Optimization Applications questions, I don't know how to find the answers. thanks.?
If c(x) is the cost of producing x units, then c(x)/x is the average cost per unit. Suppose the cost per unit. Suppose the cost of the producing x units is given by
c(x)=0.13X^3-70x^2 +100000x ans that no more than 300 units can be produced PER WEEK.
a.If the average cost is $1100 per unit, how many units are being produced?
b.what production level should be used in order to minimize the average cost per unit? What is the minimun average cost?
the answers are
a. Approximately 206units are produced.
b. the minimum value of about 577 dollars per unit occurs when about 269units are produced.

Answer 1

For (a), compute c(x)/x, which you are told is the average cost per unit; then set that result to 1100 and solve for x. You will get two answers, one of which you must discard because of the upper limit of 300 units/week. (By the way, you have a typo in the c(x) function; the last term should be 10000x, not 100000x.)

For (b), compute the derivative of the expression for c(x)/x that you got for part (a), set it to zero, and solve for x. You will get one critical point, which does lie in the interval 0 ≤ x ≤ 300. For completeness, you should compute the average cost per unit when x=0 and when x=300 as well as for the critical point (which you know is about 269), and confirm that the average cost per unit at these endpoint values for x is larger than the average cost per unit at the critical point.