I. Suppose AT & T is considering the addition of another tower in one of the fas

Question

I. Suppose AT & T is considering the addition of another tower in one of the fast growing cities to improve service and meet the growing demand. The primary location being considered will have a fixed cost of $10,000 per month and variable cost of $25 per customer served. Each customer is charged $50 on average in the area. a. What volume (number of customers) per month is required in order to break even? b. What profit would be realized on a monthly volume of 400 customers? c. What volume is needed to obtain a profit of $20,000 per month? d. What volume is needed to provide a monthly revenue of $120,000? e. What should the price be if AT&T wants to make a monthly profit of $10,000 if they have 1,000 customers? f. Plot the total cost and total revenue lines.

Explanation / Answer

Back-up Theory

Let n = number of customers served. Then, revenue, R = 50n [because Each customer is charged $50 on average in the area.]

Total cost, C = 10000 + 25n [because fixed cost is $10,000 per month and variable cost of $25 per customer served.]

For break-even n, R = C

Part (a)

We want n for which R = C. i.e., 50n = 10000 + 25n

Or n = 400 ANSWER

Part (b)

Profit that would be realized on a monthly volume of 400 customers = R – C

= (400 x 50) – {10000 + (25 x 400)}

= 0 ANSWER

Part (c)

Let N = volume needed to obtain a profit of $20,000 per month.

Then, we should have: 50N – (10000 + 25N) = 20000 or

25N = 30000

N = 1200 ANSWER

Part (d)

Volume needed to provide a monthly revenue of $120,000 = 120000/50

= 2400 ANSWER

Part (e)

Let p = the price at which AT&T will have a monthly profit of $10,000 if they have 1,000 customers. Then, we should have:

1000p – {10000 + (25 x 1000)} = 10000 or

p = 45000/1000

= $45 ANSWER

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