Economic order quantity for kayaks and books

[cjmania]

Can someone else me please I am so stuck on these questions!

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.

 

[Mark44]

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.

For the first problem I would let n = the number of times to reorder in a year, since that's the thing that you're supposed to find.

In each of these periods, it's probably reasonable to assume that the store will sell 320/n kayaks.

Now, you need to come up with an expression that represents you costs for the period -- the storage cost and the two costs associated with a reorder (the fixed cost and the cost per kayak).

So in each period the store has sold 320/n kayaks, so they don't need to store those kayaks. The remaining kayaks (320 - 320/n) will have been stored for that period, 1/n of a year, at a cost of $16/n for each kayak. When you reorder, it will cost $10 + $7 for each of the 320/n kayaks being ordered. Keep in mind that this cost is going to be incurred n times in a year.

From the above, you should be able to come up with a function C(n) that represents the total cost incurred in a year for storage and reordering kayaks. When you get this function, you should be able to use calculus to find its minimum value.

If my explanation seems difficult to follow, just pick a value for n, such as 2 (reorder twice a year, or every 6 months) and calculate what the expenses would be. Then do the same for another value of n, say 4, and calculate the expenses again. That should help you think about this problem so that you can look at it in a more abstract way with a variable number of reorder times per year.

I didn't work this problem, but I've described how I would approach it. A similar tack will probably work for the other problem.