$(5$ points$)$ Veronica operates an identical business in Beauxbatons Carriage; however,

the optimal order quantity for her business is $100$ bars, even though she has access to

the same production cost, sells it at same price as Emily in part $($a$),$ and can offload

unsold inventory in a similar manner. The difference is in the demand of Beauxbatons

students, which, unlike Hogwarts, has a pdf of $f(x)=x,$ for xin$[0,].$ With this

information, could you conclude whether $$ is larger or smaller than $\frac{1}{11250}?$ You can

explain this rigorously without calculating $.$

$(8$ points$)$ Assume that at most only $10$ unsold bars can be included into gift sets as

Bradely is worried about the reputation of Hog's Head. The rest of the unsold bars goes

to charity for benefit of house elves because of Luciana's advocacy $($ $$0$ per item$).$ Write

the expected cost function. You do not need to find the optimal solution.