A burger stall owner must make a single order for burgers. Each burger costs the owner $$13$ and

leftover burgers are marked down to $$5$ for quick sale. Loss of goodwill from customers if burgers

run out is $$\frac{28\mathrm{.}5}{?}$ burger. Estimated sales are given with the following probabilities:

$($a$)(10$ points$)$ Determine the optimal order quantity.

$($b$)(10$ points$)$ Determine the expected shortage and the expected surplus.

$($c$)(10$ points$)$ Determine the total expected cost.