Flextrola, Inc., an electronics systems integrator, is planning to design a key component for their next-generation product with Solectrics. Flextrola will integrate the component with some software and then sell it to consumers. Given the short life cycles of such products and the long lead times quoted by Solectrics, Flextrola only has one opportunity to place an order with Solectrics prior to the beginning of its selling season. Flextrola's demand during the season is normally distributed with a mean of 1,000 and a standard deviation of 600.

Solectrics' production cost for the component is $52 per unit and it plans to sell the component for $72 per unit to Flextrola. Flextrola incurs essentially no cost associated with the software integration and handling of each unit. Flextrola sells these units to consumers for $121 each. Flextrola can sell unsold inventory at the end of the season in a secondary electronics market for $50 each. The existing contract specifies that once Flextrola places the order, no changes are allowed to it. Also, Solectrics does not accept any returns of unsold inventory, so Flextrola must dispose of excess inventory in the secondary market. a. What is the probability that Flextrola's demand will be within 25 percent of its forecast? b. What is the probability that Flextrola's demand will be more than 40 percent greater than its forecast?

c. Under this contract, how many units should Flextrola order to maximize its expected profit? For parts d through i, assume Flextrola orders 1,200 units. d. What are Flextrola's expected sales?

e. How many units of inventory can Flextrola expect to sell in the secondary electronics market?

f. What is Flextrola's expected gross margin percentage, which is (Revenue - Cost)/Revenue?

g. What is Flextrola's expected profit?

h. What is Solectrics' expected profit?

i. What is the probability that Flextrola has lost sales of 400 units or more?

j. A sharp manager at Flextrola noticed the demand forecast and became wary of assuming that demand is normally distributed.

She plotted a histogram of demands from previous seasons for similar products and concluded that demand is better represented by the log normal distribution. Figure 12.7 plots the density function for both the log normal

and the normal distribution, each with mean of 1,000 and standard deviation of 600. Figure 12.8 plots the distribution function for both the log normal and the normal. Using the more accurate forecast (i.e., the log normal distribution), approximately how many units should Flextrola order to maximize its expected profit?

FIGURE 12.7 Density Function Probability 0012 0011 0010 Log Normal Distribution 0009 0008 0007 0006 0005 0004 0003 0002 0001 0,0000 Normal Distribution 0 250 500 750 000 250 500 750 2.0002.250 2.500 Demand