Question

A retailer buys 800 USB Flash Drives per year from a distributor. The retailer wants to determine how many drives to​ order, x, per shipment so that her inventory is exhausted just as the next shipment arrives. The processing fee is ​$20 per​ shipment, the yearly storage cost is ​$1.60​x, and each drive costs the retailer ​$4.45. ​

(a) Express the total yearly cost C as a function of the number x of drives in each shipment. ​
(b) Use a graphing utility to determine the minimum yearly cost and the number of drives per order that yields the minimum cost.

Answer 1

To find the total yearly cost for ordering USB flash drives, we need to consider the processing fee, storage cost, and the cost of each drive. The total yearly cost can be expressed as a function of the number of drives in each shipment. To find the minimum cost and number of drives per order, a graphing utility can be used.

Step-by-step explanation:

To determine the total yearly cost C as a function of the number of drives x in each shipment, we need to consider the processing fee, storage cost, and the cost of each drive. The processing fee is a fixed cost of $20 per shipment. The yearly storage cost is $1.60 times the number of drives in each shipment, which can be expressed as 1.60x. The cost of each drive is $4.45. Therefore, the total yearly cost can be expressed as:

C = 20 + 1.60x + 4.45 * 800 / x

To determine the minimum yearly cost and the number of drives per order that yields the minimum cost, you can use a graphing utility. By graphing the function and finding the x value that corresponds to the minimum point on the graph, you can determine the minimum yearly cost and the number of drives per order.