Suppose the total cost, TC, is the sum of two parts of costs

Question

Suppose the total cost, TC, is the sum of two parts of costs, C-A and C-B. Suppose both C-A and C-B are twice-differentiable in a variable s. Suppose further that C-A increases in s, and C-B decreases in s. a) Find the first order condition if you are to choose s to minimize the total cost, TC. Graph the minimization. b) Suppose C-A increases in a parameter, α, but the slope of C-A with respect to s does not depend on α. Suppose also C-B does not depend on α. How does an increase in the value of α affect the optimized s? Graph the changes. c) Suppose both C-A and the slope of C-A with respect to s increase in α. Suppose also C-B does not depend on α. How does an increase in the value of α affect the optimized s? Graph the changes.