Old MacDonald had a farm called Eee$-$ooh$-$eeh$-$ooh$-$Queue. On that farm he had some ducks. And on that farm he had some goats. Eee$-$ooh$-$eeh$-$ooh$-$Queue farm has to stock duck feed and goat feed for its animals.

These feed options have some nice characteristics for modeling $($and fortunately, this is realistic!$)$ The food comes in pellet form, so it is relatively long lasting. The animals are also very consistent with how much they eat, so demand for the food is near constant $---$ Old MacDonald can perfectly predict how much he needs to feed his animals each year. Plus, he orders the feed from his next door neighbor, so there's no significant lead time between when he places his order and when it is delivered.

Here are some characteristics of the two types of feed.

Duck feed:

Holding cost of $$\frac{2}{l}\frac{b}{?}$ year

Setup cost of $$\frac{6}{?}$ order

Cost to order of $$\frac{1}{l}b$

Demand of $5,000lb\frac{s}{?}$ year

Goat feed:

Holding cost of $$\frac{3}{l}\frac{b}{?}$ year

Setup cost of $$\frac{10}{?}$ order

Cost to order of $$A|lb|$

Demand of $1,666\mathrm{.}67lb\frac{s}{m}$onth

a$.(3$ points$)$ What is the optimal amount of duck feed to order? $($Fractional amounts are OK$!)$

Answer: $173\mathrm{.}21($rounding ok$)$

b$.(2$ points$)$ What is the annual inventory cost associated with the optimal order quantity of duck feed? $($Fractional amounts are OK$!)$

Answer: $346\mathrm{.}41($rounding ok$)$

c$.(3$ points$)$ What is the optimal amount of goat feed to order? $($Fractional amounts are OK$!)$ Answer: $365\mathrm{.}15($rounding ok$)$

d$.(2$ points$)$ What is the annual inventory cost associated with the optimal order quantity of goat feed? $($Fractional amounts are OK$!)$

Answer: $1095\mathrm{.}45($rounding ok$)$

e$.(3$ points$)$ A new feed product went to market which can feed both ducks and goats. It has a holding cost of $$\frac{1}{?}$ pound$/$year$,$ a setup cost of $$\frac{8}{?}$ order, and a cost to order of $$\frac{2}{l}b.$ Assuming that the ducks and goats will eat the same amount of this feed as their previous feed, what is the annual inventory$-$related cost associated with the optimal order quantity of this new feed?

Answer: $632\mathrm{.}46($rounding ok$)$