Business Calculus Minimize Inv Cost

In summary: The key step is to solve for x, which we can do by substituting the given information into the equation:C(x) = 5x + (45x) (135/x)which gives us:C(x) = 10x + 45x + 135xThe solution to this equation is x = 5. Thus, the store should order pool tables five times per year.
  • #1
KevinJay
1
0

Homework Statement


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... I am not sure how to continue. I know I have to find the derivative after, but I don't know how I would condense X
 
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  • #2
KevinJay said:

Homework Statement


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... I am not sure how to continue. I know I have to find the derivative after, but I don't know how I would condense X
 
  • #3
KevinJay said:

Homework Statement


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... I am 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 .
 

1. What is Business Calculus?

Business Calculus is a branch of mathematics that combines concepts from calculus and business applications. It is used to solve optimization problems in business and economics, such as minimizing costs and maximizing profits.

2. What is the purpose of using Business Calculus to minimize inventory costs?

The purpose of using Business Calculus to minimize inventory costs is to find the optimal level of inventory that will result in the lowest possible cost for a business. This can help businesses make more informed decisions about their inventory management and ultimately increase their profits.

3. How does Business Calculus help in minimizing inventory costs?

Business Calculus helps in minimizing inventory costs by using mathematical techniques such as derivatives and optimization to determine the most efficient level of inventory for a business. This involves finding the point at which the cost of holding inventory is equal to the cost of ordering more inventory.

4. What factors are considered when using Business Calculus to minimize inventory costs?

When using Business Calculus to minimize inventory costs, factors such as production costs, storage costs, demand for the product, and ordering costs are taken into account. These factors can vary for different businesses and can affect the optimal inventory level.

5. Are there any limitations to using Business Calculus to minimize inventory costs?

While Business Calculus is a powerful tool for minimizing inventory costs, it relies on certain assumptions and simplifications that may not accurately reflect the real-world complexities of a business. Additionally, it requires a good understanding of calculus and may not be accessible to everyone. Other factors such as market fluctuations and unexpected events can also impact the accuracy of using Business Calculus to minimize inventory costs.

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