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Ch1 ModA Solutions 1

Topics: Expected value, Probability theory, Random variable / Pages: 3 (647 words) / Published: Nov 10th, 2014
3101 MSOM
1st in-class Group Assignment (Ch 1 and Mod A)

Q1) Lake Charles Seafood makes 450 wooden packing boxes for fresh seafood per day, working in two 10-hour shifts. Due to increased demand, plant managers have decided to operate three 8-hour shifts per day instead. The plant is now able to produce 650 boxes per day. (2-points)
i. Before the change in work rules, the company's productivity = boxes/hour ii. After the change, the new productivity level = boxes/hour iii. Based on the changes made, the percent increase in productivity =. If it wished to increase its productivity by more than 18%, did it happen? _YES_.

iv. If production is increased to 800 boxes per day (with the three 8-hour shifts), the new productivity is boxes/hour.

Q2) Charles Lackey operates a bakery in Idaho Falls, Idaho. Because of its excellent product and excellent location, demand has increased by 45% in the last year. On far too many occasions, customers have not been able to purchase the bread of their choice. Because of the size of the store, no new ovens can be added. At a staff meeting, one employee suggested ways to load the ovens differently so that more loaves of bread can be baked at one time. This new process will require that the ovens be loaded by hand, requiring additional manpower. This is the only thing to be changed. (Productivity remains the same. Each worker works 160 hours per month)
If the bakery currently makes 1500 loaves per month with a labor productivity of 2.344 loaves per labor hour, then Lackey will need to add _______ worker(s) to meet the increased demand. (2-points)

Solution: Each worker works for 160 hours in a month and has a productivity of 2.344 loaves/ hour. Therefore, in a month’s time, he can produce 160*2.344 = 375.04 loaves.

Increase demand = 0.45*1500 = 675. To make 675 loaves in a month, when 1 person can make 375.04, Charles would need to hire people

Q3) There are three likely states of nature (High (50%), Medium (30%), and Low (20%) demand). If the large factory will post profits of $50,000, $25,000, and - $10,000 under these states of nature, respectively, what will be the EMV of the factory? (1-point)

EMV = 50000*0.5 + 25000*0.3 - 10000*0.2 = 30,500

Q4) A plant manager wants to know how much he should be willing to pay for perfect market research. Currently there are two states of nature facing his decision to expand or do nothing. Under favorable market conditions the manager would make $100,000 for the large plant and $5,000 for the small plant. Under unfavorable market conditions the large plant would lose $50,000 and the small plant would make $0. If the two states of nature are equally likely, how much should he pay for perfect information? (2-points)

The expected value of perfect information for Smith =

= 100,000*0.5 + 0*0.5 = 50,000
= 25,000

EVPI = 25,000

Q5) Smith Jones, Inc., is considering building a sensitive new airport scanning device. His managers believe that there is a probability of 0.35 that the ATR Co. will come out with a competitive product. If Smith adds an assembly line for the product and ATR Co. does not follow with a competitive product, Smith’s expected profit is $65,000. If Smith adds an assembly line and ATR follows suit, Smith still expects $10,000 profit. If Smith adds a new plant addition and ATR does not produce a competitive product, Smith expects a profit of $600,000, if ATR does compete for this market, Smith expects a loss of 120,000 (3-points)

Solution: The decision table for this problem is as follows:

ATR comes out with a competitive product
ATR does not follow the product
Smith adds an assembly line
Smith adds a new plant

a) Expected value for the ‘Adds an assembly line’ option is $45,750. Expected value for the ‘Adds a new plant’ option is $348,000

The alternative that provides Smith the greatest expected monetary value is ‘Adds a new plant’.

b) Using the maximax and maximin methods, the appropriate decisions are ‘Adds a new plant’ & Adds an assembly line’ respectively.

c) The expected value of perfect information for Smith = = $ 45,500

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