Question 1

A business wants to minimize its total inventory costs, which include both ordering and carrying costs. If the business orders more frequently with smaller order sizes, what is the most likely effect on the total costs?

Accepted Answer

Ordering costs will increase, but carrying costs will decrease, and total costs may not be minimized.

Question 2

Given the following scenario: A store sells 1200 cases of juice per year, with an ordering cost of $$75 per order and a carrying cost of 8 $$per case per year. What is the formula for the total cost $$C as a $$function of order size $$x$$?

Accepted Answer

$$C = \frac{1200}{x} \cdot 75 + \frac{x}{2} \cdot 8$$

Question 3

In the context of inventory control, what does the average inventory level represent if orders are evenly spaced and each order arrives just as the previous is exhausted?

Accepted Answer

One-half of the order size.

Question 4

A farmer has 204 meters of fencing to build two corrals: one square and one rectangular with length twice its width. What is the constraint equation for the total fencing used if $$x is $$the side of the square and $$w is $$the width of the rectangle?

Accepted Answer

$$4x + 6w = 204$$

Question 5

Which of the following best describes the trade-off between ordering costs and carrying costs in inventory control?

Accepted Answer

Decreasing order size increases ordering costs but decreases carrying costs.

Question 6

If a business wants to keep an average inventory of $$x$$ units and places $$n$$ orders per year, what is the relationship between the total number of units sold per year $$D$$, order size $$x$$, and number of orders $$n$$?

Accepted Answer

$$n = \frac{D}{x}$$

Question 7

Suppose the cost to store each case of juice is $$8$$ per year, and the average inventory is $$x/2. $$What is the annual carrying cost for an order size of $$x$$?

Accepted Answer

$$4x$$

Question 8

A store manager wants to minimize total inventory costs. Which calculus-based method should be used to find the optimal order size?

Accepted Answer

Set the derivative of the total cost function with respect to order size to zero and solve for order size.

Question 9

If the total cost function for inventory is $$C(x) = \frac{1200}{x} \cdot 75 + \frac{x}{2} \cdot 8$$, what is the value of $$x$$ that minimizes $$C(x)$$?

Accepted Answer

$$x = \sqrt{\frac{2 \cdot 1200 \cdot 75}{8}}$$

Question 10

A business sells 1200 units per year, with an ordering cost of $$75$$ per order and a carrying cost of $$8$$ per unit per year. What is the minimum total cost per year, rounded to the nearest dollar?

Accepted Answer

$$692$$

Question 11

In the fencing problem, if the rectangular corral has length $$2w$$ and width $$w$$, what is the area of the rectangle in terms of $$w$$?

Accepted Answer

$$2w^2$$

Question 12

Which of the following best describes the purpose of finding the Economic Order Quantity (EOQ) in inventory management?

Accepted Answer

To minimize the total cost of ordering and carrying inventory.

Question 13

If a business increases its order size, what is the effect on the average inventory level?

Accepted Answer

The average inventory level increases.

Question 14

A store manager wants to keep the average inventory at 100 units. If each order is for $$x$$ units, how many orders per year should be placed if the store sells 1200 units per year?

Accepted Answer

$$12$$

Question 15

In the context of the inventory graph provided, what does the slope of each line segment represent?

Accepted Answer

The rate at which inventory is depleted.

Business Calculus Study Notes: Further Optimization Problems (Inventory Control & Area Maximization)

Study Guide - Practice Questions

Study Guide - Flashcards