Ezra's dog, Bobos, every day eats on average $4$ pounds of kibble with a standard deviation of $1$ pound. Ezra buys the kibble from an online retailer that charges $$4$ per pound of kibble. The retailer guarantees a $2-$day delivery, and the delivery fee is equal to $$24.$ Living in a small house Ezra doesn't have too much storage space, so he estimates that keeping a pound of kibble in the cabinet essentially costs him $$0\mathrm{.}25$ per week. The retailer has two different sizes for kibble: $70-$pound bags and $100-$pound bags.

Every time a new delivery arrives, Ezra throws away any leftover kibble so that he doesn't mix new and old kibble. Also, if he runs out, he needyio replace the missing kibble with an equal amount of wet food which costs more, at $$16$ per p$$und$.$ Ezra acquires wet food from a nearby store. Therefore, wet food has no lead time or fixed delivery fees.

Of course, since feeding the dog is the bare minimum the owner should do$,$ Ezra derives no value per unit of kibble consumed by Bobos. Note that there are $365$ days, or $52$ weeks in a year.

a$)[4$ pts$]$ What is the safety stock Ezra should aim for?

Answer: $0\mathrm{.}95$ pounds.

b$)[2$ pts$]$ How much kibble on average sits in the cabinet if Ezra orders $70-$pound bags? How much kibble sits in the cabinet if he orders $100-$pound bags?

Answer:

If $70$:$35\mathrm{.}95$ pounds

If $100$:$50\mathrm{.}95$ pounds

c$)[7$ pts$]$ Should Ezra order $70-$pound bags or $100-$pound bags for each order if the goal is to minimize annual inventory costs?

Answer: $70$

d$)[1$pts$]$ How many pounds of kibble are in storage when Ezra puts in a new order?

Answer: $8\mathrm{.}95$

e$)[4$pts$]$ A competing kibble supplier reaches out to Ezra. This supplier is willing to create custom$-$made kibble bags for Bobos, as long as Ezra specifies the exact size of each bag, for a delivery fee of $$36$ for same$-$day delivery. Should Ezra pay for this service? Explain why.

Answer: No $($you need to explain why on the actual quiz$)$

Just need help understanding how they got the answers :)