Math question?

Question

Can someone help me figure out this problem please?

A bookstore is attempting to determine the economic order quantity for a popular book. The store sells 8000 copies of this book a year. The store figures that it costs $40 to process each new order for books. The carrying cost (due primarly to interest payments) is $2 per book, to be figureed on the maximum inventory during an order-reorder period. How many times should orders be places?

Answer 1

Let x be the number of times orders are placed.

The processing cost is obviously 40*x
The carrying cost is 2*(8000/x)
So the total cost is 40x + 16000/x

To minimize the cost, figure out where the derivative is zero.

40 - 16000/x^2 = 0
16000/x^2 = 40
x^2 = 16000/40 = 400
x = sqrt(400) = 20

To minimize costs, orders should be placed 20 times.

Answer 2

Let x=# of books to inventory, y=# of times to order. The cost=2*x+40*y. The constraint eqn is x*y=8000. Solve the constraint eqn for x, and substitute into the cost. (x=8000/y) => cost=2*(8000/y)+40*y. Minimize the cost by setting the derivative equal to 0. (i.e. d/dy[2*8000/y+40*y] = 0). This is true when y=20. So the store will inventory 400 books, and make a total of 20 orders.

Answer 3

Economic Order Quantity = Sqrt (2CO/i)
Where
C = Consumption per anum = 8000
O = Ordering Cost per order = $40
i = Carrying Cost per unit/Year = $2

Therefore
EOQ = Sqrt (2*8000*$40/$2)
= 566 units per order

No. of times the order should be placed
= C/EOQ
= 8000/566
= 14 or 15 times (approximately)

http://www.futureaccountant.com/process-costing/