Management Science

Cost, Revenue & Break-Even Analysis

1. Kim Davis has decided to purchase a cellular phone for her car, but she is unsure about which rate plan to select. The “regular” plan charges a fixed fee of $55 per month for 70 minutes of air time plus $0.33 per minute for any time over 70 minutes. The “executive” plan charges a fixed fee of $75 per month for 100 minutes of air time plus $0.25 per minute over 100 minutes.

a. If Kim expects to use the phone for two hours per month, which plan should she select?

b. At what level of use would Kim be indifferent between the two plans?

2. The Pastureland Dairy makes cheese, which it sells at local supermarkets. The fixed monthly cost of production is $4000 and the variable cost per pound of cheese is $0.21. The cheese sells for $0.75 per pound; however, the dairy is considering raising the price to $0.95 per pound. The dairy currently produces and sells 9000 pounds of cheese per month, but if it raises its price per pound, sales will decrease to 5700 pounds per month. Should the dairy increase the price?

3. For most products, higher prices result in a decreased demand, whereas lower prices result in an increased demand. Let

d – annual demand for a product in units

p – price per unit

Assume that a firm accepts the following price-demand relationship as being realistic:

d = 800 – 10p

where p must be between $20 and $70.

c. How many units can the firm sell at $20 per-unit price? At $70 per-unit price?

d. Show the mathematical model for the total revenue (TR), which is the annual demand multiplied by the unit price.

e. Based on other considerations, the firm’s management will only consider price alternatives of $30, $40, and $50. Use your model from part (b) to determine the price alternative that will maximize the total revenue.

f. What are the expected annual demand and the total revenue according to your recommended price?

4. A publishing company is...