Name:________________________

Learning Motivator I - Quantitative Economics 39

March 25, 1997

You will have one hour two complete this motivational exercise. Please show all of your work clearly in the space provided. Illegible writing will be marked incorrect. If you use the back of a page, indicate that you have done so on the front of the page. Good Luck!

1) [12 points] A department store has overhead costs of $250,000 and a linear total cost function. The controller has set the store’s margin policy using the example of a $140 markup on an item retailing for $500. The controller has also estimated that other variable costs (selling expenses as opposed to the cost of the good sold) on the same retail item selling for $500 are $15.

- Find the revenue, cost, and profit functions using s for sales volume.

- Find the break-even dollar volume of sales

- Draw the break-even chart.

d. What will net profit be if sales are $3,000,000.

2) [10 points] Complete the following operations:

a)

3) [10 points] If A = , what is A^{-1}?

4) [12 points] A printer quotes a price of $7,500 for printing 1000 copies of a book and $15,000 for printing 2500 copies. Assuming a linear relationship and that 2,000 books are printer:

- Find the equation relating the total cost, y, to x, the number of books printed.

- What is the variable cost?

- What is the fixed cost?

- What is the average cost per book?

e) What is the marginal cost of the last book printed?

5) [12 points] ComElectric charges its customers according to their usage of electricity. One rate it charges commercial users is as follows: a monthly customer charge of $6.00, $0.05973 energy charge per kwh for the first 2300 kwh, $0.02505 energy charge per kwh in excess of 2300 kwh, and $0.00048 conservation charge per kwh.

a) Determine the cost function and draw its graph.

b) What are the total and average charges for using 4000 kwh?

- How many kwh were used if the total charge is $254.26.

6) [10 points] What sum of money invested now at 12 percent compounded monthly will provide just enough to pay a debt of $2,500 due in 3 years?

7) [10 points] The demand curve for a product shifts from

DD: p = -0.05q + 40 to D’D’: p = -0.05q + 50.

Compute the horizontal and vertical shifts and write interpretive descriptions of the numbers.

8) [12 points] Florida Juice Company wants to make a new 30-gallon mixture of apple, cranberry, and grapefruit juice for its restaurant clients. The new mixture should have a sugar content of 11 percent and an acidity rating of 3 percent. Each gallon of apple juice costs $1.25 and has a sugar content of 12 percent and an acidity rating of 4 percent. The per-gallon cost of cranberry juice is $1.00 with a sugar content of 10 percent and an acidity rating of 2 percent, while the per-gallon cost of grapefruit juice is $0.90 with a sugar content of 9 percent and an acidity rating of 1 percent.

- What is the solution in arbitrary-variable form?

b) If the new mixture should be made at a minimum cost, how much of each juice should be used and what is the cost?

9) [12 points] Fran will make 20 equal semiannual deposits to an account earning 8 percent compounded semiannually. Then, after the last deposit, she will use the amount in the account to establish an ordinary annuity earning 6 percent compounded annually which will provide her with $10,000 at the end of each year for 5 years. How much should Fran’s semiannual deposit be?