# Business Calculus Minimize Inv Cost

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?[/B] ## Homework Equations Yearly Carrying Cost =$10 (x/2) -> 5x
Yearly Reorder Cost = 27+18x(135/x)

## 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

Mark44
Mentor

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?[/B] ## Homework Equations Yearly Carrying Cost =$10 (x/2) -> 5x
Yearly Reorder Cost = 27+18x(135/x)
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.
KevinJay said:

## 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

Ray Vickson
Homework Helper
Dearly Missed

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?[/B] ## Homework Equations Yearly Carrying Cost =$10 (x/2) -> 5x
Yearly Reorder Cost = 27+18x(135/x)

## 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

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 .