Antipasti is a company that makes antipasti and dips made with local products. They are renowned for their antipasto being fresh, made every week

$($

presumably they are produced at the beginning of that week

$)$

$.$

$$The demand they observe weekly can be approximated with a normal distribution of average

$50$

$$and standard deviation of

$5$

$$per week. On average, a

$5$

$$oz antipasto has a unit cost of $

$1\mathrm{.}30$

$$and sells for $

$3\mathrm{.}50$

$.$

$$Any antipasto left over at the end of the week is discarded; although the container is washed and recycled, thus recovering $

$0\mathrm{.}30$

$$per

$5$

$$oz container.

Questions

Part

$($

a

$)$

$$Determine how much the antipasto should be made per week.

Part

$($

b

$)$

$$Using that order size

$($

i

$.$

e

$.$

$$the one calculated in Part

$($

a

$))$

$$for the next

$40$

$$weeks$,$ determine the average cost per week of

$$

overage

$$

$$and underage if demand behaved as follows in those next weeks