Problems:
Minimum cost and maximum profit
1) The cost per unit produced at a certain facility is represented by the function UC = 2x^2 - 10x + 50, where x is in thousands of units produced. For what value of x would unit cost be minimized (other than zero)? What is the minimum cost at this volume? Show that the value found is truly a minimum.
2) Advertising expenditures have been found to relate to profit approximately in accordance with the function P = x^3 - 100x^2 + 3125x, where x is the expenditure in thousands of dollars. What advertising expenditure would produce the maximum profit? What profit is expected at this expenditure? Show that the derived result is truly a maximum.