Question

Bike Inc. owns a bike service station in Florida, where the climate is warm year-round. Customers have often expressed the need, especially during summer, for a cold drink facility at the station. The Cody Beverage Company has offered to lease Bike Inc a cold drink vending machine for $400 per month plus $0.40 per can of cold drinks. Bike Inc. would sell each can of cold drink for $1.50.

A regression equation estimated based on 30 observations gave the following prediction of sales of cans of cold drinks:

Sales units=0.70(number of customers) + 60 per month. The standard error of the estimate is 80 cans.

Required: You must provide all the detailed supporting calculations

1. Assuming that Bike Inc. expects 1,400 customers in June; what are the best estimates of number of cans of cold drinks sold, and income for the month of June?
2. What range of income can Bike Inc. expect with 95% confidence in June?
3. What is the required number of customers Bike Inc. must have to be 95% confident to make a profit of $645 in the month of June?     
4. What is the probability that Bike Inc would earn zero income in June?   

Answer 1

(a) No. of customers = 1400.

No. of cans sold = 1400 x 0.70 + 60 = 1040

Income = 1040 x 1.5 = $ 1,560

(b) 95% confidence interval corresponds to approx 2 standard error, so for June, the sales can range between 1040-8-x2 to 1040 + 80 x 2, i.e., between 880 and 1200 cans

The corresponding income can range between 880x1.5 and 1200x1.5, i.e., between $ 1,320 and $ 1,8000

(c) Let N be the no of cans sold.

Profit = N x (1.50-0.4) - 400

N = (Profit + 400) / (1.10) = (645+400)/1.10 = 950

This is lower 95% confidence interval. So the estimated sales = 950 + 2 x 80 = 1110 cans

Customers = (1110 - 60)/0.70 = 1500

(d) We see that the sales can't be below 60, with nil customers. Hence the income will be 60 x 1.5 = $ 90 per month at a minimum. Hence the probability of ahving a Zero income is 0.