Question

A toy manufacturer expects to sell 4536 games in a year. The games cost $20 each plus a fixed delivery cost of $140 per order. If it cost $5 to store a game for a year, find the order size and the number of orders that minimizes inventory costs.  

Answer 1

Here say we ship x no. of games per order (order size)and total y no. of orders was given so total cost for delivery would be 20xy+140y

Where 140y for orders 20x for games for each order, y no. of orders so 20xy for games

Also here is to notify that we already have xy no. of games and to store each game we need 5$ per year for each game to store so we need 5xy to the whole set of games (no. of games is xy)

So to perform the whole process we need total 20xy+140y+5xy amount of money    20xy+140y+5xy=25xy+140y.............(1),

Now according to given problem we expect to sell 4536 no. of games in a year but we'll ship x no. of games per order and no. of orders would be y so xy=4536..............(2)

So, from (1) and (2) we get total 140y+25×4536 amount of money so total money would be least if y is least and y atleast would be 1 so in that case x would be 4536 ( as xy=4536)

So toy manufacturer company need atleast 140+25×4536=113,450$

So, no. of order would be 1 order size would be 4536 that minimize inventory cost