$3.$ Marketing research indicates that the average consumer visits a supermarket $2\mathrm{.}5$ times per week.$$ On each visit the average market basket is $$45,$ on which the store earns a $15\%$ margin. Customers are very loyal but there is a churn rate of $10\%$ per year. When discounting cash flows, managers assume the interest rate is $10\%$ per year.$$

$$

$3$a$.$ What is the weekly margin obtained from a typical customer?$$ $$\_\_\_\_\_$

$$

$$

$$

$$

$3$b$.$ How long can the store assume that the average customer will stay shopping at its store?

$$

$\_\_\_\_\_$ years

$$

$$

$$

$$

$$

$$

$3$c$.$ What is the total discounted margin obtained over the lifetime of a typical customer?

$$$$\_\_\_\_\_$

$$

$$

$$

$$

$$

$3$d$.$ What is the minimum number of new customers required to justify a new ad campaign costing $$175,000?$

$\_\_\_\_\_$customers