Question

A shoe store orders shoes from the manufacturer and sells them at a mall. Storing shoes at the store costs $3 per shoe pair for a year. When reordering shoes from the manufacturer, there is a fixed cost of $25 per order as well as $5 per shoe pair. The retail store sells 4500 shoe pairs each year. Find a function that models the total inventory costs as a function of x x the number of shoe pairs in each order from the manufacturer.

Answer 1

Answer:

the function that models the total inventory costs as a function of x is;

$( $\frac{112500}{x}$ + ($\frac{3}{2}$)x )

Step-by-step explanation:

Given the data in the question;

cost of storing the shoes ( Holding cost ) = $ 3 per year

ordering cost ( Co ) fixed = $ 25 per order

cost of each pair = $ 5 per shoe pair

Total demand = 4500 shoe pairs

Total Inventory cost = Holding cost Ordering cost

so

Total Inventory cost = $\frac{4500}{x}$( $ 25) + $\frac{1}{2}$× $3 × x

Total Inventory cost = $( $\frac{4500*25}{x}$ + ($\frac{3}{2}$)x )

Total Inventory cost = $( $\frac{112500}{x}$ + ($\frac{3}{2}$)x )

Therefore, the function that models the total inventory costs as a function of x is; $( $\frac{112500}{x}$ + ($\frac{3}{2}$)x )