SPC produces plastic sheets. The capital cost for holding 1 thousand pounds of plastic sheets is $10. The company estimated that the inventories (in thousand pounds) it needs to hold during the four quarters in a year are 300, 900, 200, and 400, respectively. It costs $20 to store and handle 1 thousand pounds of plastic sheets for a quarter in a public warehouse. Private warehouse requires a yearly lease, with a cost of $40 per square foot (which can hold 1 thousand pounds of plastic sheets). In addition, SPC incurs a material handling costs of $2 per thousand pounds of plastic sheets stored each quarter when using a private warehouse.

(a) What is the cost SPC incurs if only public warehouse is used?

(b) What is the cost SPC incurs if only private warehouse is used?

(c) Develop a plan to use a combination of public and private warehouses to reduce the cost.