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Name: Surname: ID: BUS 336 Data and Decisions II Sample Final Exam December , 2019 You have 160 minutes for this exam. Please do not write on this paper. Show all your solutions on final exam booklet. Please write your name and ID on your exam booklet and on top of every page you used in the booklet. This exam consists of 6 questions that worth a total of 40 points. QUESTION 1 An olive oil producer produces using raw oils from ). Regions A,B,C can provide 300,400 and 500 barrels of oil. Each type has 250 barrels of demand. Barrel of Region A costs 10 dollars, Region B costs 20 dollars and Region C costs 30 dollars. Any type cannot exceed 10% Region A oil, each type must have at least 30% Region C oil. Formulate an LP model that decides minimum cost plan with the amounts of Region A,B,C oils on Types A,B,C,D, while meeting the demand and obeying the above describe conditions. QUESTION 2 In the following business situations, please write the method you would use to solve the problem (don’t solve). You can suggest a , , of LP, regression or . For forecasting please also suggest the forecasting method that would be the best fit. (Examples are going to be similar to these exam questions in short descriptions, or midterm or suggested exercises except the fact that you won’t need to solve them but only to spot which method to use to solve) QUESTION 3 You gather your monthly spending data to follow your finances and you would like to be able to forecast your spending for next month. Here are 10 months of data. Try with , ; calculate s. Show all forecasts. With the method with lower MAD, calculate also the forecast for nexth (11th) month. [𝐹𝑡+1 = 𝐹𝑡 + 𝛼(𝑌𝑡 − 𝐹𝑡 ) ]

Month 1 2 3 4 5 6 7 8 9 10

Forecast with Spending MA 500 525 476 600 420 520 600 550 480 540

Forecast with exp smoothing 450

QUESTION 4

Regression Statistics R Square 0.712104377 Adjusted R Square X Standard Error X Observations 397

S=根号下MSE

ANOVA df Regression Residual Total

Intercept X Variable 1 X Variable 2 X Variable 3 X Variable 4 X Variable 5

5

X

391 X 396

X

Coefficients 40.48117815 1.47933458 66.58211581 39.9178522 23.34651079 5.60335241

SS MS SSR 204356.4 X MSR XSSE X MSE SST X Standard Error 3.007479 2.4871 2.524351 2.674846 2.458493 2.524686

F

Significance F X 2.4E-103

t Stat P-value -13.4602 3.36E-34 0.594803 0.552319 -26.3759 8.2E-89 14.92342 3.53E-40 9.496269 2.21E-19 2.219426 0.027031

a. Fill the Regression Statistics and ANOVA tables. (Adjusted R2, Standard Error, all three df values, SSR, SSE, MSR, MSE, F-stat) b. Is the model significant? Can you find significance a level in which this model would not be insignificant? c. Perform significance test for all of the variables (including intercept) at 1% level.

QUESTION 5 Below there is the sensitivity table of the solution of the model in 1st question. (In the exam there will be a separate example in such a question but here I give this as a hint to the constraints in Q1) Constraints Cell $C$11 $D$11 $E$11 $C$7 $C$8 $C$9 $C$10 $E$7 $E$8 $E$9 $E$10 $F$7 $F$8 $F$9

Name Available Region A oil Available Region B oil Available Region C oil Maximum Region A oil in Type A Maximum Region A oil in Type B Maximum Region A oil in Type C Maximum Region A oil in Type D Minimum Region C oil in Type A Minimum Region C oil in Type B Minimum Region C oil in Type C Minimum Region C oil in Type D Demand Type A Demand Type B Demand Type C

$F$10

Demand Type D

Final Shadow Constraint Value Price R.H. Side 100 0 300 400 0 400 500 0 500 25 0 0 25 0 0 25 0 0 25 0 0 75 1 0 125 0 0 75 0 0 225 0 0 250 0.3 250 250 0 250 250 0 250 250

0

250

Allowable Allowable Increase Decrease 1E+30 200 50 0 1800 0 50 0 50 0 50 0 180 0 50 75 50 1E+30 50 75 150 1E+30 0 83.33333333 0 83.33333333 0 83.33333333 -5.68434E1E+30 14

They consider several options to increase profitability. Please write your suggested course of action and the expected change in profit for the following problems. a.) What happens to cost if Demand of Type D increase to 260? b.) What happens to cost if Demand of Type D increase to 260 while demand of Type A decrease to 240? c.) There is a new type that they can start to produce. It will not have any minimum or maximum usage of region oils to add as constraint, but its introduction will decrease the demand of type A to 200. The cost of adoption of new type is considered to be around $50. Should this new type be produced?

QUESTION 6 During an office hour, a varying number of students visit and ask me questions. I gathered the data to measure interval between arrivals and how long it takes for me to answer the question. My office hour lasts for . If there is a student ,I to solve their question but I ’ after they leave. Set up a simulation model to calculate iteration, variables, relations between variables etc.).

I see per office hour (Describe one

(RAND() generates a uniformly distributed random variable between 0-1, you can use this function in your expressions) Interval(minutes) Probability 5 0.20 10 0.10 15 0.30 20 0.40

Time to solve question (minutes) Probability 10 0.10 15 0.20 20 0.30 25 0.30 30 0.10...