A retail drug chain purchases a newly developed drug in pill form from a pharmaceutical firm and sells it to the public. During FDA testing, it was determined that the drug's active ingredient expires quickly and the retailer can$$t sell pills which are purchased more than $30$ ?days earlier. The selling price per $30-$day supply $($bottle$)$ ?of pills is $$250.$ ?Unsold pills have no value and are disposed of at no cost$.$ ?

The marketing forecast for sales is $50,000$ ?bottles per month with standard deviation of $8,000,$ ?distributed normally. The pharmaceutical firm sells the drug to the retail chain for $$90$ ?per bottle.

The pharmaceutical firm has offered the retailer the following option. Return unsold bottles to the pharmaceutical firm. The pharmaceutical will reprocess the pills to make them good again and distribute them free to those who can$$t afford them. This action will not affect the demand of the retailer. The retailer assigns a $$15$ ?goodwill value for each bottle donated to the needy. The retailer has to pay the shipping cost, which is negligible and amounts to few cents per bottle.

What is the cost of overage $($overestimating demand$)$ ?by one bottle of the drug under the new option?

?

?

$75\mathrm{.}00$

$108\mathrm{.}00$

$62\mathrm{.}50$

$90\mathrm{.}00$

$45\mathrm{.}25$

What service level $($probability of satisfying demand$)$ ?should the retail drug chain provide under the new option?

$0\mathrm{.}8611$

$0\mathrm{.}4945$

$0\mathrm{.}7188$

$0\mathrm{.}5613$

$0\mathrm{.}6809$

What is the Z value that corresponds to the service level in the previous question?

$2\mathrm{.}08$

$0$

$1\mathrm{.}96$

$0\mathrm{.}47$

$-0\mathrm{.}45$