Help with Questions on Worksheet - Reorder, Inventory Costs

[cjmania]

Can someone give me a hand with these questions because I am really stuck on these!

I am stuck on both these questions, I have no idea where to begin I was given a worksheet which our instructor will review with us but I would like to know how to do them before class. I finished most of it but this I am stuck on. Can someone please help me to better understand these Thank You:

1) An outdoor sports company sells 320 kayaks per year. It costs $16 to store one kayak for a year. Each reorder costs $10, plus an additional $7 for each kayak ordered. How many times per year should the store order kayaks in order to minimize inventory costs?




2) A bookstore has an annual demand for 79,000 copies of a best-selling book. It costs $.20 to store one copy for one year, and it costs $50 to place an order. Find the optimum number of copies per order.

 

[Tac-Tics]

I am stuck on both these questions, I have no idea where to begin I was given a worksheet which our instructor will review with us but I would like to know how to do them before class. I finished most of it but this I am stuck on. Can someone please help me to better understand these

For the first one, plot a timeline in units of months or something. Take a 12-month section of this timeline. You know that 320 kayaks are sold in this period, and because it's not stated in the problem, we're going to assume that they are purchased at a constant rate (so, for some reason, kayaks are in demand in both summer *and* winter). So you can divide the timeline into 320 intervals of equal length.

By symmetry, intuition suggests that the store's kayak orders will will also be evenly spaced. Furthermore, they will each have the same number of kayaks per order, and that each new order is placed when the store runs out of kayaks in stock. These are necessary assumptions as the problem does not specify these critical details.

So you have n orders of k kayaks in a given year, and we can reason that n*k = 320. From here, you can easily figure out the total annual cost of ordering kayaks.

On top of the cost of ordering new kayaks, we have to account for the cost to store kayaks in inventory. Again, the problem doesn't say much on the subject, so we're going to assume "$16 per year" is an evenly distributed cost, so it might as well be written "$(16/12) = $1.33 per month" or "roughly four cents a day". How long we need to store each kayak will conveniently be equal to the time interval between kayak orders, and it's not hard to figure out the total annual cost of maintenance.

Add the annual cost of orders and the annual cost of maintenance, and this is your total annual cost.

The hard part is over, and you can use calculus for the rest. The total annual cost is a function of n, the number of orders per year. The solution to the entire problem is the value for n which minimizes total annual cost.

Hopefully the number comes out as a positive integer. There were a lot of assumptions, and some of them only make total sense with continuous quantities, not discrete objects like canoes.

The second problem is solved the exact same way using different constants (79000 copies instead of 320 kayaks)... except it doesn't seem to list the price of a book.