Part $3$: Ordering Raw Materials for Manufacturing

A manufacturing company needs to order raw materials for processing into a finished product that it sells.

These materials are available exclusively in $1,000-$pound increments and are subject to the daily fluctuations of market prices. The anticipated cost for these materials averages $$36$ per pound, with a variability $($standard deviation$)$ of $$4$ per pound. Orders are consolidated, meaning each batch within a single order is procured at an identical rate. For instance, acquiring $10$ batches at $$35$ per pound would culminate in an expenditure of $$350,000.$ There are fixed production costs of $$40,000$ per order. There is only one order per month.

During the production phase, the conversion of raw material to the finished product results in a net loss of material. The expected conversion efficiency stands at $89\%,$ though this rate can fluctuate, historically ranging from $80\%$ to $94\%.$ To illustrate, utilizing $10,000$ pounds of raw material at a $92\%$ efficiency yields $9,200$ pounds of the final product.

The sale price for the finished goods is set at $$50$ per pound. Consequently, selling $9,200$ pounds of product would generate revenue amounting to $$460,000,$ thereby achieving a profit of $$70,000($$$460,000$ in sales minus $$350,000$ in raw material costs and $$40,000$ in fixed costs$).$

Your task is to construct a Monte Carlo simulation model to analyze the profit of various raw material order volumes. Consider only a single month.

Assume the firm is able to sell all the final product it produces. Run your model with at least $2,000$ iterations.