a manufacturer has daily production costs of C=4000-30x+0.5x where C is the total cost in dollars and x is the number of units produced. (a) How many units should be produced each day to yield a minimum cost? (b) What is the minimum cost?

Answer 1

C has a typo. One of the terms should be x^2, I expect.

If so, then C is just a parabola, and its minimum cost is at the vertex.