Simple Saris is a retailer of womens fashion They purchase g

Simple Saris is a retailer of women\'s fashion. They purchase garments in lots from a supplier and then sell them to customers in their store. It costs $4 to store one garment for a year. To reorder more garments from their supplier, Simple Saris pays a fixed fee of $6 per lot as well as a per garment fee of $3. They sell 1750 garments each year.

Find a function that models their total inventory costs (in dollars) as a function of x x the lot size for each of their orders from the supplier.

Solution

let  x be the lot size for each of their orders from the supplier.

number of orders = 1750/x

caryying cost = yearly storage cost per item * average number of items carried

4*x/2 = 2x

yearly reordering cost = 6*(1750/x)

Inventory cost = 6*(1750/x) + 2x