Question 1

Earl Shell owns his own Sno-Cone business and lives 30 miles from a beach resort. The sale of Sno-Cones is highly dependent upon his location and upon the weather. At the resort, he will profit $120 per day in fair weather, $10 per day in bad weather. At home, he will profit $70 in fair weather, $55 in bad weather. Assume that on any particular day, the weather service suggests a 40% chance of foul weather.
a. Construct Earl's decision tree.
b. What decision is recommended by the expected value criterion?

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Question 2

The EMV of a decision with three states of nature is $33,000. If the profit/value under the states of nature A, B, and C is $10,000, $20,000, and $50,000 and states B and C have equal probabilities, determine the likelihood of state of nature A.

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Question 3

The EMV of a decision with three states of nature is $50. If the profit/value of A is 1/3 of B and B is 1/3 of C, determine the profit from A if B and C have an equal chance of occurring that combined is twice the chance of A occurring.

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Question 4

Miles is considering buying a new pickup truck for his lawn service firm. The economy in town seems to be growing, and he is wondering whether he should opt for a subcompact, compact, or full-size pickup truck. The smaller truck would have better fuel economy, but would sacrifice capacity and some durability. A friend at the Bureau of Economic Research told him that there is a 30% chance of lower gas prices in his area this year, a 20% chance of higher gas prices, and a 50% chance that gas prices will stay roughly unchanged. Based on this information, Miles has developed a decision table that indicates the profit amount he would end up with after a year for each combination of truck and gas prices.
 $$\begin{array} { | l | c | c | c | } 
\hline &  { \text { States of Nature } } \
\hline \text { Alternatives } & \text { Lower gas prices } & \text { Gas prices unchanged } & \text { Higher gas prices } \
\hline \text { probability } & .3 & .5 & .2 \
\hline \text { Subcompact } & 16,000 & 21,000 & 23,000 \
\hline \text { Compact } & 15,000 & 20,000 & 22,000 \
\hline \text { Full size } & 18,000 & 19,000 & 6,000 \
\hline
\end{array}$$ 
Calculate the expected monetary value for each decision alternative. Which decision yields the highest EMV?

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Question 5

A local business owner is a bit uncertain of the demand forecast, and is timidly approaching the capacity decision for a business he is about to open. Here's how he describes the decisions that confront him over the next two years."First, I have to choose between building a large plant initially and building a small one that has room to expand. Or I could rent now, and decide whether to build next year. That one, too, could be the large version or the small. If I build small, then after one year, I can review how good business was, and decide whether to expand. If I build large, there is no further option to enlarge."Do not concern yourself with probabilities or payoff values .Simply draw the tree that illustrates the manager's decision alternatives and the chance events that go along with them. Use standard symbols for decision tree construction, and label all parts of your diagram carefully. To simplify, assume that business in the first year, and in the second, can be only "good" or "bad."

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Question 6

A do-it-yourself homeowner is installing a new toilet. While installing the toilet he must decide on what kind of connecting pipe he will install to the water supply. There are two available options, one that has a shut-off valve in case of a leak and a cheaper one without the shut-off valve. Suppose that the shut-off valve pipe costs an extra ten dollars and that the homeowner must buy one of the two.
a. Draw a decision tree for this scenario, labeling the cost of a leak as X and the chance of a leak as P.
b. If the chance of a leak causing household damage is 1%, at what $ amount of household damage is the owner neutral on which pipe to buy?
c. If the cost of a leak would be $10,000 what is the maximum % chance to leak at which the homeowner would prefer to buy the cheaper pipe?
d. If the cost of a leak is $1,000 and the chance to flood .1% which pipe should the homeowner buy?

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Question 7

The campus bookstore sells highlighters that it purchases by the case. Cost per case, including shipping and handling, is $200. Revenue per case is $350. Any cases unsold will be discounted and sold at $175. The bookstore has estimated that demand will follow the pattern below
 $$\begin{array} { | c | c | } 
\hline \text { Demand level } & \text { Probability } \
\hline 10 \text { cases } & 20 \text { percent } \
\hline 11 \text { cases } & 20 \text { percent } \
\hline 12 \text { cases } & 40 \text { percent } \
\hline 13 \text { cases } & 15 \text { percent } \
\hline 14 \text { cases } & 5 \text { percent } \
\hline
\end{array}$$ 
a. Construct the bookstore's payoff table.
b. How many cases should the bookstore stock in order to maximize profit?
c. How would your answer differ if the clearance price were not $175 per case but $225 per case?
 (It is not necessary to re-solve the problem to answer this.)

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Question 8

A poker player is considering three different options after his opponent bet 200 before him. If the player folds, he will lose instantly. If the player calls, he figures he will win half the time. If he raises he figures that the opposing player will not re-raise him, but rather will either call or fold. He figures the opposing player will call only ¼ of the time, folding the other ¾ of the time. If the opposing player calls his raise, he figures he will never win. The pot size is 1,000 (including the opposing player's bet).
a. Draw a decision tree for this scenario including the information provided in part b.
b. Suppose that the player is thinking of raising to $400 (he will put in 200 to match the opponent's bet and another 200 as a raise, his opponent would then have to put in 200 more to call the raise). Is this the best option or should he instead call or fold?
c. At what raise size is the player's EMV of a raise equivalent to simply calling?

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Question 9

Daily sales of bread by Salvador Monella's Baking Company follow the historical pattern shown in the table below. It costs the bakery 50 cents to produce a loaf of bread, which sells for 95 cents. Any bread unsold at the end of the day is sold to the parish jail for 25 cents per loaf. Construct the decision table of conditional payoffs. How many loaves should Sal bake each day in order to maximize contribution?
 $$\begin{array} { | l | c | c | c | c | c | } 
\hline \text { Demand } & 400 & 500 & 600 & 700 & 800 \
\hline \text { Probability } & .20 & .20 & .40 & .15 & .05 \
\hline
\end{array}$$

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Question 10

Earl Shell owns his own Sno-Cone business and lives 30 miles from a beach resort. The sale of Sno-Cones is highly dependent upon his location and upon the weather. At the resort, he will profit $110 per day in fair weather, $20 per day in foul weather. At home, he will profit $70 in fair weather, $50 in foul weather. Assume that on any particular day, the weather service suggests a 60% chance of fair weather.
a. Construct Earl's payoff table.
b. What decision is recommended by the expected value criterion?
c. What is the EVPI?

Accepted Answer

The answer of Earl Shell owns his own Sno-Cone business...

Question 11

Bratt's Bed and Breakfast, in a small historic New England town, must decide how to subdivide (remodel) the large old home that will become their inn. There are three alternatives: Option A would modernize all baths and combine rooms, leaving the inn with four suites, each suitable for two to four adults. Option B would modernize only the second floor; the results would be six suites, four for two to four adults, and two for two adults only. Option C (the status quo option) leaves all walls intact. In this case, there are eight rooms available, but only two are suitable for four adults, and four rooms will not have private baths. Below are the details of profit and demand patterns that will accompany each option. Which option has the highest expected value?
 Annual profit under various demand patterns
$\begin{array}{|l|c|c|c|c|}
\hline & \text { Capacity } & \mathrm{p} & \text { Average } & \mathrm{p} \
\hline \text { A (Modernize all) } & \$ 90,000 & .5 & \$ 25,000 & .5 \
\hline \text { B (Modernize } & & & & \
 \text {2 (nd) } & \$ 80,000 & .4 & \$ 70,000 & .6 \
\hline \mathrm{C} \text { (Status Quo) } & \$ 60,000 & .3 & \$ 55,000 & .7 \
\hline
\end{array}$

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Question 12

Steve Gentry, the operations manager of Baja Fabricators, wants to purchase a new profiling machine (it cuts compound angles on the ends of large structural pipes used in the fabrication yard). However, because the price of crude oil is depressed, the market for such equipment is down. Steve believes that the market will improve in the near future and that the company should expand its capacity. The table below displays the three equipment options he is currently considering, and the profit he expects each one to yield over a two-year period. The consensus forecast at Baja is that there is about a 30% probability that the market will pick up "soon" (within 3 to 6 months) and a 70% probability that the improvement will come "later" (in 9 to 12 months, perhaps longer).
 $$\begin{array}{l}
\text { Profit from Capacity Investment (in Dollars) }\
\begin{array} { | l | c | c | } 
\hline \text { Equipment Option } & \begin{array} { c } 
\text { Market picks up } \
\text { "soon" } \
p = 0.30
\end{array} & \begin{array} { c } 
\text { Market picks up } \
\text { "later" } \
p = 0.70
\end{array} \
\hline \text { Manual Machine } & - 120000 & 210000 \
\hline \text { NC Machine } & 140000 & 160000 \
\hline \text { CNC Machine } & 200000 & - 200000 \
\hline
\end{array}
\end{array}$$ 
a. Calculate the expected monetary value of each decision alternative.
b. Which equipment option should Steve take?

Accepted Answer

The answer of Steve Gentry, the operations manager of Baja...

Question 13

A toy manufacturer makes stuffed kittens and puppies which have relatively lifelike motions. There are three different mechanisms which can be installed in these "pets." These toys will sell for the same price regardless of the mechanism installed, but each mechanism has its own variable cost and setup cost. Profit, therefore, is dependent upon the choice of mechanism and upon the level of demand. The manufacturer has in hand a forecast of demand that suggests a 0.2 probability of light demand, a 0.45 probability of moderate demand, and a probability of 0.35 of heavy demand. Payoffs for each mechanism-demand combination appear in the table below.
 $$\begin{array} { | l | c | c | c | } 
\hline \text { Demand } & \text { Wind-up action } & \text { Pneumatic action } & \text { Electronic action } \
\hline \text { Light } & \$ 250,000 & \$ 90,000 & - \$ 100,000 \
\hline \text { Moderate } & 400,000 & 440,000 & 400,000 \
\hline \text { Heavy } & 650,000 & 740,000 & 780,000 \
\hline
\end{array}$$ 
Construct the appropriate decision tree to analyze this problem. Use standard symbols for the tree. Analyze the tree to select the optimal decision for the manufacturer.

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The answer of A toy manufacturer makes stuffed kittens and...

Question 14

Suppose a manufacturing plant is considering three options for expansion. The first one is to expand into a new plant (large) , the second to add on third-shift to the daily schedule (medium) , and the third to do nothing (small) . There are three possibilities for demand. These are high, medium, and low with each having an equal likelihood of occurring. Suppose that the profits for the expansion plans are as follows (respective to high, medium, low demand). The large expansion profits are $100000, $10000, -$10000, the medium expansion choice $40000, $40000, $5000 and the small expansion choice $15000, $15000, $15000. Calculate the EMV of each choice. Which of the expansion plans should the manager choose?

Accepted Answer

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Question 15

A toy manufacturer has three different mechanisms that can be installed in a doll that it sells. The different mechanisms have three different setup costs (overheads) and variable costs and, therefore, the profit from the dolls is dependent on the volume of sales. The anticipated payoffs are as follows.
 $$\begin{array} { | l | c | c | c | } 
\hline & \text { Light Demand } & \begin{array} { c } 
\text { Moderate } \
\text { Demand }
\end{array} & \text { Heavy Demand } \
\hline \text { Probability } & 0.25 & 0.45 & 0.3 \
\hline \text { Wind-up action } & \$ 325,000 & \$ 190,000 & \$ 170,000 \
\hline \text { Pneumatic action } & \$ 300,000 & \$ 420,000 & \$ 400,000 \
\hline \text { Electrical action } & - \$ 400,000 & \$ 240,000 & \$ 800,000 \
\hline
\end{array}$$ 
a. What is the EMV of each decision alternative?
b. Which action should be selected?
c. What is the expected value with perfect information?
d. What is the expected value of perfect information?

Accepted Answer

The answer of A toy manufacturer has three different mechanisms...

Question 16

Miles is considering buying a new pickup truck for his lawn service firm. The economy in town seems to be growing, and he is wondering whether he should opt for a subcompact, compact, or full-size pickup truck. The smaller truck would have better fuel economy, but would sacrifice capacity and some durability. A friend at the Bureau of Economic Research told him that there is a 30% chance of lower gas prices in his area this year, a 20% chance of higher gas prices, and a 50% chance that gas prices will stay roughly unchanged. Based on this information, Miles has developed a decision table that indicates the profit amount he would end up with after a year for each combination of truck and gas prices. Develop a decision tree for this situation and indicate which type of truck he should select.
 $$\begin{array} { | l | c | c | c | } 
\hline &  { \text { States of Nature } } \
\hline \text { Alternatives } & \text { Lower gas prices } & \text { Gas prices unchanged } & \text { Higher gas prices } \
\hline \text { probability } & .3 & .5 & .2 \
\hline \text { Subcompact } & 16,000 & 19,000 & 21,000 \
\hline \text { Compact } & 15,000 & 20,000 & 22,000 \
\hline \text { Full size } & 24,000 & 19,000 & 6,000 \
\hline
\end{array}$$

Accepted Answer

The answer of Miles is considering buying a new pickup...

Question 17

The campus bookstore sells stadium blankets embroidered with the university crest. The blankets must be purchased in bundles of one dozen each. Each blanket in the bundle costs $65, and will sell for $90. Blankets unsold by homecoming will be clearance priced at $20. The bookstore estimates that demand patterns will follow the table below.
a. Build the decision table.
b. What is the maximum expected value?
c. How many bundles should be purchased?
 $$\begin{array} { | l | l | } 
\hline \text { Demand level } & \text { Probability } \
\hline 1 \text { bundle } & 10 \text { percent } \
\hline 2 \text { bundles } & 30 \text { percent } \
\hline 3 \text { bundles } & 50 \text { percent } \
\hline 4 \text { bundles } & 10 \text { percent } \
\hline
\end{array}$$

Accepted Answer

The answer of The campus bookstore sells stadium blankets embroidered...

Quiz 21: Decision-Making Tools

The EMV of a decision with three states of nature is $33,000. If the profit/value under the states of nature A, B, and C is $10,000, $20,000, and $50,000 and states B and C have equal probabilities, determine the likelihood of state of nature A.

The EMV of a decision with three states of nature is $50. If the profit/value of A is 1/3 of B and B is 1/3 of C, determine the profit from A if B and C have an equal chance of occurring that combined is twice the chance of A occurring.