Question

To examine the effectiveness of its four annual advertising promotions, a mail order company has sent a questionnaire to each of its customers, asking how many of the previous year's promotions prompted orders that would not have otherwise been made. The accompanying table lists the probabilities that were derived from the questionnaire, where X is the random variable representing the number of promotions that prompted orders. If we assume that overall customer behavior next year will be the same as last year, what is the expected number of promotions that each customer will take advantage of next year by ordering goods that otherwise would not be purchased?

Expected value =
a. 2.289
b. 3.201
c. 4.107
d. 1.842
A previous analysis of historical records found that the mean value of orders for promotional goods is 32 dollars, with the company earning a gross profit of 20% on each order. Calculate the expected value of the profit contribution next year.

Expected value =
a. $8.20
b. $6.40
c. $14.6496
d. $9.60
The fixed cost of conducting the four promotions is estimated to be 14000 dollars with a variable cost of 2.5 dollars per customer for mailing and handling costs. What is the minimum number of customers required by the company in order to cover the cost of promotions? (Round your answer to the next highest integer.)

Answer 1

The expected number of promotions that each customer will take advantage of next year is 3.201. The expected value of the profit contribution next year is $6.40. The minimum number of customers required to cover the cost of promotions is 7600 (rounded to the next highest integer).

Step-by-step explanation:

The expected number of promotions that each customer will take advantage of next year by ordering goods that otherwise would not be purchased can be calculated using the formula for expected value:

Expected value = Σ(X × P(X))

where X is the random variable and P(X) is the probability for that value. In this case, the random variable X represents the number of promotions that prompted orders. The calculations using the given probabilities would result in an answer of 3.201.

The expected value of the profit contribution next year can be calculated using the formula:

Expected value = Σ(X × P(X))

where X is the random variable and P(X) is the probability for that value. In this case, the random variable X represents the profit contribution. The calculations using the given mean value of orders and gross profit percentage would result in an answer of $6.40.

The minimum number of customers required to cover the cost of promotions can be calculated by dividing the fixed cost by the contribution per customer. The contribution per customer can be calculated by subtracting the variable cost per customer from the mean value of orders and multiplying by the gross profit percentage. In this case, the calculation would result in a minimum number of customers of 7600 (rounded to the next highest integer).