A chemical company produces a certain organic chemical in batches.

The annual demand rate for this chemical is $100,000$ pounds. The

demand can be considered to be known with certainty and the rate

does not change with time. The fixed cost of producing a batch is

$$500.$ The variable cost of production is $$2\mathrm{.}00$ per pound. There is

a backorder cost of $$5\mathrm{.}00$ per pound per year, and no fixed cost of

a backorder, i$.$e$.,$ t $=0.$ Determine the optimal batch size and the

optimal number of backorders to incur