Chapter 6.4, Problem 74E

(a)

To determine

The average daily inventory.

Answer to Problem 74E

The average daily inventory is 300 drums.

Explanation of Solution

Given information:

Inventory function,

  $I\left(x\right)=450-\frac{x^2}{2}$

Calculations:

According to FTC (Fundamental Theorem of Calculus):

The average value for 30 − day period,

  $\begin{array}{l}\frac{1}{b-a}{\displaystyle {\int }_a^{b}I\left(x\right)}dx=\frac{1}{30-0}{\displaystyle {\int }_0^{30}\left(450-\frac{x^2}{2}\right)dx}\\ =\frac{1}{30}\times {\left(450x-\frac{x^3}{6}\right)|}_0^{30}\\ =\frac{1}{30}\times \left(450\times 30-\frac{{\left(30\right)}^3}{6}\right)\\ =300\text{drums}\end{array}$

Thus,

The average daily inventory is 300 drums.

(b)

To determine

The average daily holding cost.

Answer to Problem 74E

The average daily holding cost is $6.

Explanation of Solution

Given information:

Inventory function,

  $I\left(x\right)=450-\frac{x^2}{2}$

The holding cost for one drum is $\$0.02/\text{day}$ .

Calculations:

From Part (a) result,

We have

The average number of drums is 300.

According to statement,

Each drum’s holding cost is $0.02.

Now,

  $\begin{array}{l}\text{Avg}\text{.}\text{holding}\text{cost}=\text{Avg}\text{.}\text{number}\text{of}\text{drums}\times \text{Each}\text{drum's}\text{holding}\text{cost}\\ =300\text{drums}\times \$0.02\text{per}\text{drum}\\ \text{=}\text{\$6}\end{array}$

Thus,

The average daily holding cost is $6.