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.
X 0 1 2 3 4
P(X) 0.075 0.24 0.39 0.162 0.133
The fixed cost of conducting the four promotions is estimated to be 17000 dollars with a variable cost of 2 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 up to the next highest integer.)
Break even point =
You can't break even unless there is a profit associated with each sale, all you listed were the costs.
net profit=income(sales)-cost(sales)-fixedcost
How do you do this?
To find the break-even point, we need to calculate the total cost of conducting the promotions and divide it by the average profit per customer.
The total cost of conducting the promotions is given by:
Total cost = Fixed cost + (Variable cost per customer * Number of customers)
Given:
Fixed cost = $17000
Variable cost per customer = $2
Let's calculate the average profit per customer:
Average profit per customer = Revenue per customer - Cost per customer
From the given probabilities, we can calculate the revenue per customer for each possible number of promotions:
Revenue per customer = (Number of promotions * Probability of that number of promotions) * Profit per order
Given:
Profit per order = $0 (Since it states that the promotions only prompted orders that would not have otherwise been made, implying no additional profit)
Using the table, we can calculate the revenue per customer for each number of promotions:
Revenue per customer = (0 * 0.075) + (1 * 0.24) + (2 * 0.39) + (3 * 0.162) + (4 * 0.133)
Now, we need to find the minimum number of customers required to cover the cost of promotions. We can set up the following equation:
Total cost = Average profit per customer * Number of customers
Solving for the number of customers:
Number of customers = Total cost / Average profit per customer
Substituting the values:
Number of customers = (Fixed cost + (Variable cost per customer * Number of customers)) / ((0 * 0.075) + (1 * 0.24) + (2 * 0.39) + (3 * 0.162) + (4 * 0.133))
We can plug in different values for the number of customers and solve for the smallest integer value that satisfies the equation.
Let me calculate the break-even point for you.
To determine the break-even point for the company, we need to calculate the total cost of promotions and compare it to the revenue generated by those promotions.
First, let's calculate the total cost of promotions. The fixed cost of conducting promotions is given as $17,000. In addition, there is a variable cost of $2 per customer for mailing and handling costs.
Next, we need to calculate the revenue generated by the promotions. The revenue can be calculated by multiplying the number of customers who made a purchase due to promotions by the average revenue per customer.
To calculate the number of customers who made a purchase due to promotions, we need to multiply each probability (P(X)) by its corresponding number of promotions (X) and sum them up.
(0 * 0.075) + (1 * 0.24) + (2 * 0.39) + (3 * 0.162) + (4 * 0.133) = 1.597
So, the average number of customers who made a purchase due to promotions is approximately 1.597.
To calculate the average revenue per customer, we need to know the revenue generated per customer on average. This information is not provided, so we cannot calculate the exact break-even point without this information.
However, we can calculate the minimum number of customers required to cover the cost of promotions by assuming a certain average revenue per customer. Let's assume the average revenue per customer is $50.
Now we can calculate the break-even point:
Break-even point = Total cost of promotions / Average revenue per customer
Total cost of promotions = Fixed cost + (Variable cost per customer * Average number of customers who made a purchase due to promotions)
Total cost of promotions = $17,000 + ($2 * 1.597) = $17,000 + $3.194 = $20,194
Average revenue per customer = $50
Break-even point = $20,194 / $50 = 403.88
Rounding up to the next highest integer, the minimum number of customers required to cover the cost of promotions is 404.
Therefore, the minimum number of customers required by the company in order to cover the cost of promotions is 404.