A chemical plant produces sodium bisulfate in $100kg$ bags. Demand for this product is $20$ tons

per day. The capacity for producing this product is $50$ tons per day. Setup cost is $$400,$ and

storage and handling costs are $$200$ per ton per year. The company operates $200$ days a year.

$($Note: $1$ ton$=1,000$ kg$).$

$($a$)$ What is the optimal number of bags per production run?

$($b$)$ What would the average inventory level be for this lot size?

$($c$)$ Determine the approximate length of a production run, in days.

About how many production runs per year would there be$?$

$($e$)$ How much could the company save annually in inventory control cost if the setup cost

could be reduced to $$200$ per production run

and the optimal production quantity is recalculated and used?