Answer:
35,000 units
Step-by-step explanation:
Total revenue is:
[tex]R = -x^3+39x^2+945x[/tex]
The maximum revenue is attained at the production level for which the derivate of the revenue function is zero:
[tex]R = -x^3+39x^2+945x\\R'=0=-3x^2+78x+945\\x=\frac{-b\pm\sqrt{78^2-(4*(-3)*945)} }{-6}\\x_1=35\\x_2=-9[/tex]
Since production cannot be negative, revenue will be at a maximum when x = 35, or when the production level is 35,000 units.
