Thread: Question related to expected value

Hi,
Thanks in advance for any help you can provide.

The question is:
A previous analysis of historical data of advertising campaigns found that the mean value of orders for promotional goods is $12.50, with the company earning a gross profit of 20% on each order. The fixed cost of conducting the four promotions next year is estimated to be $15 000, with a variable cost of $3.00 per customer for mailing and handling costs.

How large a customer base must the company have to cover the cost of the promotions?

So far I have

0.20 x $12.50 = 2.50 gross profit per item
15 000 / 2.50 = 6000 customers.

The correct answer is 9231 customers.

I don't know how to incorporate the 3.00 variable in the calculation / where I'm going wrong?

Thanks in advance,
Tom

Total cost = fixed cost + variable cost. Your total cost will be 15000+3y where y is size of the customer base

Not sure if the $12.50 is the total average order or average sales price per item, but if it is the former, it looks like a $ loser even without the $15 K fixed cost:

$12.50 x .2 = $2.50 gross profit per order with a $3.00 cost per customer...not good unless you can expect more than 1 order per customer that you send this to.

If it is the latter, then you need to specify how many items each customer purchases.

I'm stumped , sorry!