consider the following cost function.\na. find the average cost and marginal cost functions.\nb. determine…

Explanation:

Step1: Recall average - cost formula

The average cost function $\overline{C}(x)$ is given by $\overline{C}(x)=\frac{C(x)}{x}$, where $C(x)$ is the cost function. Given $C(x)=1500 + 0.8x$, then $\overline{C}(x)=\frac{1500 + 0.8x}{x}=\frac{1500}{x}+0.8$.

Step2: Recall marginal - cost formula

The marginal cost function $C'(x)$ is the derivative of the cost function $C(x)$. Since $C(x)=1500 + 0.8x$, and the derivative of a constant $k$ is $0$ and the derivative of $ax$ with respect to $x$ is $a$ (where $a = 0.8$ in this case), then $C'(x)=0.8$.

Step3: Calculate average and marginal cost at $x = a$

When $x=a = 2200$, the average cost $\overline{C}(2200)=\frac{1500}{2200}+0.8=\frac{15}{22}+0.8=\frac{15}{22}+\frac{8}{10}=\frac{15\times5}{22\times5}+\frac{8\times11}{10\times11}=\frac{75}{110}+\frac{88}{110}=\frac{75 + 88}{110}=\frac{163}{110}\approx1.48$. The marginal cost $C'(2200)=0.8$.

Step4: Interpret the values

The average cost $\overline{C}(2200)\approx1.48$ represents the average cost per unit when $2200$ units are produced. It is the total cost of producing $2200$ units divided by the number of units. The marginal cost $C'(2200) = 0.8$ represents the additional cost of producing one more unit when $2200$ units have already been produced.

Answer:

a. $\overline{C}(x)=\frac{1500}{x}+0.8$ b. $\overline{C}(2200)\approx1.48$, $C'(2200)=0.8$ c. The average cost of $1.48$ is the per - unit cost when 2200 units are produced. The marginal cost of $0.8$ is the cost of producing one more unit when 2200 units have been produced.