# Business Calculus Minimize Inv Cost

1. Oct 18, 2015

### KevinJay

1. The problem statement, all variables and given/known data
A sporting goods store sells 135 pool tables per year. It costs $10 to store one pool table for a year. To reorder, there is a fixed cost of$27 per shipment plus $18 for each pool table. How many times per year should the store order pool tables, and in what lot size, in order to minimize inventory costs? 2. Relevant equations Yearly Carrying Cost =$10 (x/2) -> 5x
Yearly Reorder Cost = 27+18x(135/x)

3. The attempt at a solution
C(x) = 5x + (45x) (135/x)

Am I doing this right? I can't tell since I messed up when I was taking my notes... Im not sure how to continue. I know I have to find the derivative after, but I don't know how I would condense X

2. Oct 19, 2015

### Staff: Mentor

It's always a good idea to explicitly state what any variable represents. For this problem 'x' could be the number of pool tables to order in a shipment, or it could be the number of times per year to reorder.

3. Oct 19, 2015

### Ray Vickson

This is a standard Economic Order Quantity (EOQ) model, as found in any Operations Research textbook, or on-line; see, eg.,
https://en.wikipedia.org/wiki/Economic_order_quantity .