Quiz

Prob.01Assume that each of you put 1000 VND into a pig bank;Next, each of you pick one number between 1 and 100. The average of all the numbers (you and your classmates

picked) is calculated, and multiple it by 60% and get number X;

Whoever picks the number that is closest to this number X will get all the money and will have full score for this prob.

The number of student in this class is: Hint: It is important for you to guess which number other

students are likely to choose.

Ex: Class has 4 students A, B, C, D. Student A chose 20, B chose 50, C chose 70, D chose 100.

The Avg. Value is: (20+50+70+100)/4= 60 60*60%= 36So, B is the winner.

Quiz

Prob. 02 (Bottled Water game)Set up Payoff table and determine saddle point for the following

problem. Players: Evian, Perrier Each company has a fixed cost of $5000 per period, regardless of

salesThey are competing for the same market, and each

must chose a high price ($2/bottle), and a low price ($1/bottle)

At $2, 5000 bottles can be sold for $10,000At $1, 10000 bottles can be sold for $10,000If both companies charge the same price, they split the

sales evenly between themIf one company charges a higher price, the company

with the lower price sells the whole amount and the higher price sells nothing

Payoffs are profits – revenue minus the $5000 fixed cost

Quiz 03Prob.01An investor is going to purchase one of three types of real estate:

an apartment building, an office building, or a warehouse. The two future states of nature that will determine how much profit the investor will make are either good economic conditions or bad economic conditions. The profits that will result from each decision given these two states of nature are summarized below:

Purchase Good Economy Poor EconomyDecisionApt Bldg $ 50,000 $ 30,000Office Bldg 90,000 -40,000Warehouse 40,000 10,000

Determine the best alternative for each of 5 criteria.Determine the best alternative for each of 5 criteria.

Prob. 2: Determine EMV, EVwPI, EVPI and EOL for Prob. 01 when the Prob. 2: Determine EMV, EVwPI, EVPI and EOL for Prob. 01 when the probabilities of good and bad economy are 0.6 and 0.4 respectivelyprobabilities of good and bad economy are 0.6 and 0.4 respectively

Quiz 04Quiz 04Find the best alternativeFind the best alternative

Mark M. Upp has just been fired as the university bookstore manager for setting prices too low (only 20 percent above suggested retail). He is considering opening a competing bookstore near the campus, and he has begun an analysis of the situation. There are two possible sites under consideration. One is relatively small, while the other is large. If he opens at Site 1 and demand is good, he will generate a profit of $50,000. If demand is low, he will lose $10,000. If he opens at Site 2 and demand is high, he will generate a profit of $80,000, but he will lose $30,000 if demand is low. He also has the option of not opening either. He believes that there is a 50 percent chance that demand will be high. Mark can purchase a market research study. The probability of a good demand given a favorable study is 0.8. The probability of a good demand given an unfavorable study is 0.1. There is a 60 percent chance that the study will be favorable.

a. Construct the decision tree for Mark. Should Mark use the study? Why?

b. What is the maximum amount Mark should be willing to pay for this study?

Quiz (25 mins)Quiz (25 mins)

Quiz 05Quiz 05

Exponential smoothing is used to forecast automobile battery sales. Exponential smoothing is used to forecast automobile battery sales. Two values of alpha are examined, alpha = 0.8 and alpha = 0.5. Two values of alpha are examined, alpha = 0.8 and alpha = 0.5. Evaluate the accuracy of each smoothing constant by computing Evaluate the accuracy of each smoothing constant by computing

absolute deviation and MAD. absolute deviation and MAD.

Assume that the forecast for January was 22 batteries Assume that the forecast for January was 22 batteries

Quiz 05 SolutionQuiz 05 Solution Exponential smoothing is used to forecast automobile battery sales. Exponential smoothing is used to forecast automobile battery sales.

Two values of alpha are examined, alpha = 0.8 and alpha = 0.5. Two values of alpha are examined, alpha = 0.8 and alpha = 0.5. Evaluate the accuracy of each smoothing constant by computing Evaluate the accuracy of each smoothing constant by computing

absolute deviation and MAD. absolute deviation and MAD.

Assume that the forecast for January was 22 batteries Assume that the forecast for January was 22 batteries

On the basis of this analysis, a smoothing constant of alpha = On the basis of this analysis, a smoothing constant of alpha = 0.8 is preferred to alpha = 0.5 because it has a smaller MAD0.8 is preferred to alpha = 0.5 because it has a smaller MAD

Upon retirement, Mr. Klaws started to make two types of children's wooden toys in his shop, Wuns and Toos. Wuns yield a variable profit of $9 each and Toos have a contribution margin of $8 each. Even though his electric saw overheats, he can make 7 Wuns or 14 Toos each day. Since he doesn't have equipment for drying the lacquer finish he puts on the toys, the drying operation limits him to 16 Wuns or 8 Toos per day. Solve this problem.

Quiz (25 mins)Quiz (25 mins)

Quiz 06Quiz 06

Hot dog mixture in 1000-pound batches.Hot dog mixture in 1000-pound batches.

Two ingredients, Two ingredients, chickenchicken ($3/lb) and beef ($3/lb) and beef ($5/lb).($5/lb).

Recipe requirements:Recipe requirements:

at least 500 pounds of at least 500 pounds of chickenchicken

at least 200 pounds of beefat least 200 pounds of beef

Ratio of chicken to beef must be at least 2 to Ratio of chicken to beef must be at least 2 to 1.1.

Determine optimal mixture of ingredients Determine optimal mixture of ingredients that will minimize costs.that will minimize costs.

Hint.: You are required to set up the Linear Hint.: You are required to set up the Linear Programing model. You don’t need to solve it.Programing model. You don’t need to solve it.

Step 1:Step 1:

Identify decision variables.Identify decision variables.

xx11 = lb of chicken in mixture (1000 lb.) = lb of chicken in mixture (1000 lb.)

xx22 = lb of beef in mixture (1000 lb.) = lb of beef in mixture (1000 lb.)

Step 2:Step 2:

Formulate the objective function.Formulate the objective function.

Minimize Z = $3xMinimize Z = $3x11 + $5x + $5x22

where Z = cost per 1,000-lb batchwhere Z = cost per 1,000-lb batch $3x$3x11 = cost of chicken = cost of chicken

$5x$5x22 = cost of beef = cost of beef

SolutionSolutionExample Problem No. 1 (2 of 3)Example Problem No. 1 (2 of 3)

SolutionSolutionExample Problem No. 1 (3 of 3)Example Problem No. 1 (3 of 3)

Step 3:Step 3:

Establish Model ConstraintsEstablish Model Constraints xx11 + x + x22 = 1,000 lb = 1,000 lb

xx11 500 lb of chicken 500 lb of chicken xx22 200 lb of beef 200 lb of beef

xx11/x/x22 2/1 or x 2/1 or x11 - 2x - 2x22 0 0 xx11, x, x22 0 0

The Model: Minimize Z = $3xThe Model: Minimize Z = $3x11 + 5x + 5x22

subject to: xsubject to: x11 + x + x22 = 1,000 lb = 1,000 lb xx11 50 50

xx22 200 200 xx11 - 2x - 2x22 0 0 xx11,x,x22 0 0