Use the following problem to answer the next $9-21$ questions.

$$A retail drug chain purchases a newly developed drug in pill form from a pharmaceutical firm and sells it to the public.$$ The drug is unique in the sense that its active ingredient expires quickly and the retailer can$$t sell pills which are purchased more than $30$ days earlier. The selling price per $30-$day supply $($bottle$)$ of pills is $$340.$ Unsold pills have no value and are$$ disposed of at no cost$.$

The marketing forecast for sales is $120,000$ bottles per month with standard deviation of $20,000,$ distributed normally. The pharmaceutical firm sells the drug to the retail chain for $$110$ per bottle.

What is the cost of underage $($underestimating demand$)$ by one bottle of the drug?

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

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

The order quantity which will maximize the drug chain expected profit is$$

Group of answer choices

$109,157$ bottles

$145,982$ bottles

$129,157$ bottles

$99,433$ bottles

$163,009$ bottles