# A Manufacturer's Production Policy

The manufacturer of a particular bicycle model has the following costs associated with the management of the product's inventory. In particular, the company currently maintains an inventory of 1000 units of this bicycle model at the beginning of each year. If X units are demanded each year and X is less than 1000, the excess supply, 1000 - X units, must be stored until next year at a cost of $50 per unit. If X is greater than 1000 units, the excess demand, X - 1000 units, must be purchased separately at an extra cost of $80 per unit. Assume that the annual demand (X) for this bicycle model is normally distributed with mean 1000 and standard deviation 75.

a. Find the expected annual cost associated with managing potential shortages or surpluses of this product. (Hint use simulation to approximate the answer. An exact solution using probability arguments is beyond the level of this book.)

b. Find two annual total cost levels, equidistant from the expected value frond in part a. such that 95% of all costs associated with managing potential shortages or surpluses of this product are between these values. (Continue to use simulation)

c. Comment on this manufacturer's annual production policy for this bicycle model in light of you findings in part b.

Please use the attached template.

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#### Solution Preview

Please see the attached Excel file. A simulation is operationalized using the random number generation function along with normal distribution. I have rounded the numbers as number of units cannot be a fraction.

Note: All answers here are based on the simulation to the left.

Part ...

#### Solution Summary

The expected annual costs for a bicycle model are determined.