Chapter 11.2, Problem 26E

(a)

To determine

To calculate: The cost function $C\left(x\right)$, marginal cost function $C\text{'}\left(x\right)$ and average cost function $\overline{C}\left(x\right)$ such that $10$ carpenters are currently building a house with cost function $C=15,000+50k^2+60x^2$ where k is the number of carpenters and x is the number of electricians.

(b)

To determine

To calculate: The value of $C^{\prime }\left(15\right)$ and $\overline{C}\left(15\right)$ such that $10$ carpenters are currently building a house with cost function $C=15,000+50k^2+60x^2$ where k is the number of carpenters and x is the number of electricians. Also, determine whether the average cost is increasing or decreasing as electrician’s increases.