A company needs 50,000 items during a year. It costs $1000 to set up each production run and each item costs $22 to produce. It also costs $4 per year to store an item.

a. 2 pts If x items are in each production run, how many production runs are needed each year?

b. 4 pts What is the total cost of production if x items?

c. 2 pts Using the inventory control cost model, what is the total cost of storage?

d. 8 pts Using the inventory control cost model, find the number of items in each production run that will minimize the total cost for the company. Be sure to show that the value you found corresponds to the minimum cost.