Chapter 2.7, Problem 22E

(a)

To determine

The cost of manufacturing $60$ units of goods, where $C(x)$ is the cost function for a manufacturer in dollars, $x$ is the number of units of goods produced and $C$, $C\text{'}$ and $C\text{'}\text{'}$ are the functions as below.

(b)

To determine

The marginal cost when $40$ units of goods are manufactured, where $C(x)$ is the cost function for a manufacturer in dollars, $x$ is the number of units of goods produced and $C$, $C\text{'}$ and, are the functions as below.

(c)

To determine

At what level of production is the cost $\$1200$. Where $C(x)$ is the cost function for a manufacturer in dollars, $x$ is the number of units of goods produced and $C$, $C\text{'}$, and $C\text{'}\text{'}$ are the functions as below.

(d)

To determine

At what level(s) of production is the marginal cost $\$22.50$. Where $C(x)$ is the cost function for a manufacturer in dollars, $x$ is the number of units of goods produced and $C$, $C\text{'}$, and $C\text{'}\text{'}$ are the functions as below.

(e)

To determine

The level of production where the marginal cost has the least value and the marginal cost at this level. Where $C(x)$ is the cost function for a manufacturer in dollars, $x$ is the number of units of goods produced and $C$, $C\text{'}$, and $C\text{'}\text{'}$ are the functions as below.