Question: Each machine at a certain factory can produce 50 units per hour. The setup cost is $80 per machine, and the operating cost is $5 per hour. How many machines should be used to produce 8,000 units at the least possible cost? The answer has to be a whole number. If it is not then the least possible cost is the value of the target function at the integer nearest the answer, which is smallest. The critical value here is not an integer, but that is still the value you should list. The minimum cost, however, is the smallest value found at one of the two closest integers, mentioned in the previous sentence.

Target function f(x):__ ______
Domain of f(x):___ _____
Domain of f(x):__________
Exact value of 2nd derivative at critical value of x= __________
Max. or Min. value of f(x)___________
(value of f(x) at one of the two closest integers.)