Problem $1(20$ points$)$

"Gollee those cats sure go through a lot of food," Geoff exclaimed as he saw the shopping list pad that had been pre$-$printed with the words "cat food" a the top. He pondered a different approach to shopping for the furry little darlings, reviewed his shopping records, and discovered the following. The price of cat food has held steady at $89$ cents per can. Despite feigning indifference, each of the seven cats nibbles their way through an average of one can per day, three hundred sixty five days a year. The price of gasoline has held constant at $$3\mathrm{.}50$ per gallon and his pickup uses a gallon each way to the cat food store. The cost to hold a can of cat food is $10\%$ of the unit price.

$$

$1)$ Determine the economic order quantity for cat food$\mathrm{.}2$

$2)$ Determine the average number of orders per year if Geoff adopts an EOQ policy.

$3)$ Determine the annual setup cost if Geoff follows an EOQ policy to obtain cat food.

$4)$ Determine the combined cost of goods and inventory policy if Geoff decides to follow the economic order quantity model

$5)$ Determine the numbers of days elapsed in$-$between trips to the cat food store if Geoff wisely elects to follow an EOQ policy for obtaining cat food.