Quantitative Methods

t)o 0"9 flrubta."n s 3- 161 ? 3-AF

102 CHAPTER 3 . DECISION ANALYSIS

unl'avorable. Ken will sul1'er a loss ol'$200,000. Bul Kcn has always becn tr very optimistic dccision maker.

(a) What type of decision is Ken facing'? (b) What decision criterion should he use? (c) What altcrnalivc is bcst'l

Althou.qh Ken Brown (discussed in Problern 3-17) is

the principal owner of Brou'n Oil, his brother Bob is cledited with n:aking the company a frnancial suc- cess. Bob is vice prcsident of linance. Bob attributes his succcss to his pessimistic attitude about bttsiness

. and lhc oi1 industry. Civen the inlormation {l'om Problern 3-17, it is tikely that Bob will arrive at a ditTerent decision. Wl.rat dccision critcriotr should Bob use, and what alternative will he sciect? The Lubricanl is an cxpensivc oil ncwslcttcr to which many oil giants suhscribe. including Ken Brown (see Problem 3- l7 for details). ln the last issue. the letter described how the dernand fbr oil products would be extrenrely high. Apparently. the Anrerican consunler will continue to use oil products even if'the price of thesc products doubles. Indeed, one o1'the articles in lhe Lubricant stales thirt the chalces of'a lavorable markct fbl oil producls was 70%,. whilc thc chancc ol'an unfavorable market was only 30%. Ken would like to use these probabilities in determining the hest

decision.

(a) What dccision moticl should Lrc used? (b) What is the optir.nal decision? (c) Kcn believes that the $300,000 ligure for the Sub

100 with a fa'"orable market is too high. How much lower would this figr.rre have to be fbr Kcn to change his decision made in part h'!

0.3-18

3-20 Mickey Lawson is cousidering investing some rlroney that he inherited. The following payofr table

. gives the profits that would be realized during the next year 1or each of three inveslment alternatives Mickey is considering:

STATE OF NATURE

3-22 lAllen Young has always been proud of his personai investmenl strategies and has done very wcll over thc past sevcral ycars. Ile- invcsls primarily in the stock market. Over the past several months, how- ever, Allen has become very concerned about the stock market as a good investment. ln some cases, it would have been better for Allen to have his money in a bank than in the rnarket. Duling the next year. Allen must decide whether to invest $10.000 in the stock market or in a cortilicale ol'deposit (CD) at an intcrcst ratc of 97'. [f thc market is good. Allen bc- Iieves that he coulcl get a l4(/a relurn on his money. With a lair market, he expects to get an 87c return. If the market is bad, he will most likely get no return at all-in other words. the return would be 07 . Allen estimates that the probability of a good market is 0.:1. the probability of a tair market is 0.4, and the probability oi a bad market is 0.2. and hc wishes to maximize his long-run average return.

(a) Develop a decision tahle for this problel.r. (b) What is the best decision'l

3-23 In Problem 3-22, you helped Allcn Young detcrmine the best investment strategy. Now. Young is thinking about paying lbr a stock market newsletter. A friend ofYoung said that these types o1'letters could predict

vL:ry accurately whether the market would be good. ttir, or poor. Therr, based on thesc predictions' Allen could makc bettcr invcstmcnt dccisions.

(a) What is the mosl that Allen would be willing to pay fbr a newsletter?

(h) Young now believcs that a gurd markct will give a return of only I I %' instcad of l4c/o. Will this infbrmation change the amount that Allen would be willing to pay for the newsletter? If yiitrr an- swer is yes. determine the most that Alien would be willing to pay, given this new infbrnration.

3-2:l Today's Electronics specializes in manuficturlng modern electronic components. It also builds the equipment that produces the components. Phyllis Weinberger, who is responsible for advisin-u the president ofToday's Electronics on electronic tnantt- facturing cquipment, has developed the following table concenring a proposed lacility:

PROTTT ($)

DECISION GOOD AUTERNATT!'E ECONOMY

POOR ECONOMY

St<,rck market

Bonds

CDs

Prohahility

80,000

30,000

23,000

0.5

*20,000

20.000

23,000

0.5

STRONG MARKET

FAIR POOR MARKET MARKET

(a) What decision would maximize expected protits? (b) What is the rnaximum amount that should bc

paid fbr a pcrfect fbrecast of the economy?

Develop an opportunity loss table {br the investment problem that Mickc'y Lawson laces in Problem 3-20. What decision would minimizc the expected oppor- tunity loss'? What is the nrinimum EOL?

(a) Develop an opportunity loss table. (b) What is the minimax regret decision?

Large lacility

Medium-sizcd facility

Small facility

No facility

-550,000

300,000

200.000

0

110,000 -310.000 129.000 - r 00,000

100.000 *32,000

00

Qtantitative Analysis for MdlagemenL Twelfth Edition, by Barry Render, Ralph M. Stair, Michael E. Hanna, and Trevor S. Hale. Published by Prentice Hall. Copyright @ 2015 by Pearson Education, lnc.

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