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

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

$(
`(112500)/(x)` + (
`(3)/(2)`)x )

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 =
`(4500)/(x)`( $ 25) +
`(1)/(2)`× $3 × x

Total Inventory cost = $(
`(4500*25)/(x)` + (
`(3)/(2)`)x )

Total Inventory cost = $(
`(112500)/(x)` + (
`(3)/(2)`)x )

Therefore, the function that models the total inventory costs as a function of x is; $(
`(112500)/(x)` + (
`(3)/(2)`)x )