Question

a company orders and uses 8,960 boxes of plastic bags. each order has a fixed shipping cost of $140 and an additional cost of $2 per box of plastic bags. to store a box for a full year costs $2. what is the optimal number of orders the company should make each year? do not include units with your answer.

Answer 1

To find the optimal number of orders, calculate the total cost for each potential number of orders and find the minimum.

Step-by-step explanation:

To determine the optimal number of orders the company should make each year, we need to calculate the total cost for each possible number of orders. Let's assume the number of orders per year is 'x'.

The fixed shipping cost for each order is $140, and there is an additional cost of $2 per box of plastic bags.

We know that the company uses 8,960 boxes of plastic bags per year. So the total cost can be calculated as:

Total Cost = Fixed Shipping Cost + Additional Cost per Box of Plastic Bags

= ($140 * x) + ($2 * 8,960)

To store a box for a full year costs $2. This is a fixed cost that doesn't depend on the number of orders.

Therefore, we don't need to include it in our calculation of the total cost.

Now, we can find the optimal number of orders by minimizing the total cost function. We can do this by taking the derivative of the total cost function with respect to 'x', setting it equal to zero, and solving for 'x'.