2nd Edition

ISBN: 9781260242423

Author: CACHON

Publisher: MCG

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Forecasting is the process of predicting the future based on the past and the present data and circumstances. In other words, forecasting is the act of making a detailed analysis of future events based on the decisions made in the past as well as the pre…

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Chapter 13, Problem 7PA

Goop Inc. needs to order a raw material to make a special polymer. The demand for the polymer is forecasted to be normally distributed with a mean of 250 gallons and a standard deviation of 100 gallons. Coop sells the polymer for $25 per gallon. Goop purchases raw material for $10 per gallon and must spend $5 per gallon to dispose of all unused raw material due to government regulations. (One gallon of raw material yields one gallon of polymer.) If demand is more than Goop can make, then Goop sells only what it has made and the rest of the demand is lost.

a. How many gallons should Goop purchase to maximize its expected profit? [LO13-1]
b. Suppose Goop purchases 150 gallons of raw material. What is the probability that it will run out of raw material? [LO13-2]
c. Suppose Goop purchases 300 gallons of raw material. What are the expected sales (in gallons)? [LO13-2]
d. Suppose Goop purchases 400 gallons of raw material. How much should it expect to spend on disposal costs (in dollars)? [LO13-2]
e. Suppose Goop wants to ensure that there is a 92 percent probability that it will be able to satisfy its customers’ entire demand. How many gallons of the raw material should it purchase? [LO13-3]

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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Solution Summary: The author determines the number of gallons that must be purchased to maximize the expected profit.

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