These are multiple choice questions

Use this information to answer questions 1 to question 2

Consider the following

time series data:

Week 1 2 3 4 5 6

Value 24 13 20 12 19 23

1. (10 points) Compare three week moving average forecast with exponential smoothing

forecast using ( = 0:2). Which appears to provide better forecast based on MSE?

(a) Three week moving average provides better forecast because MSE for three week

moving average is more than exponential smoothing.

(b) Three week moving average provides better forecast because MSE for three week

moving average is less than exponential smoothing.

(c) Exponential smoothing provides better forecast because MSE for exponential smooth-

ing is more than three week moving average.

(d) Exponential smoothing provides better forecast because MSE for exponential smooth-

ing is less than three week moving average.

2. (10 points) Compare exponential smoothing forecast using ( = 0:2) with exponential

smoothing forecast using ( = 0:3). Which provides a better forecast using MSE?

(a) Exponential smoothing forecast using ( = 0:2) provides better forecast because

its MSE is higher.

(b) Exponential smoothing forecast using ( = 0:2) provides better forecast because

its MSE is lower.

(c) Exponential smoothing forecast using ( = 0:3) provides better forecast because

its MSE is higher.

(d) Exponential smoothing forecast using ( = 0:3) provides better forecast because

its MSE is lower.

3)(7 points) Find the optimal integer valued solution to the following problem:

max 0:25X + 0:50Y + 3Z

0:8X + 0:2Y 3

1:0X + 1:5Y + 3:0Z 6

1:0X + 0:6Y + 2:0Z 4

X + Y + Z 6

X; Y;Z 0

(a) (0,2,4)

(b) (2,0,4)

(c) (4,0,2)

(d) (4,2,0)

4)(8 points) The best selection of plant size depends on how the marketplace reacts to the

new product line. To conduct an analysis, marketing management has decided to view

the possible long-run demand as low, medium or high. The following payo table shows

the projected prot in millions of dollars:

Long-Run Demand

Low Medium High

Plant Size

Small, d1 150 200 200

Large, d2 50 200 500

Recommend a decision based on the use of the optimistic, conservative and minimax

regret approaches.

(a) Large plant size for optimistic approach. Small plant size for conservative and

minimax regret approach.

(b) Large plant size for optimistic and minimax regret approach. Small plant size for

conservative approach.

(c) Small plant size for optimistic approach. Large plant size for conservative and

minimax regret approach.

(d) Small plant size for optimistic and minimax regret approach. Large plant size for

conservative approach.

5. (5 points) Find the optimal mixed strategy solution for the following 2 x 2 game:

Player B

b1 b2

Player A

a1 -1 2

a2 4 -3

(a) Player A should choose strategy a1 with probability 0.7 and player B should choose

strategy b1 with probability 0.5.

(b) Player A should choose strategy a1 with probability 0.6 and player B should choose

strategy b1 with probability 0.58.

(c) Player A should choose strategy a1 with probability 0.75 and player B should choose

strategy b1 with probability 0.6.

(d) Player A should choose strategy a1 with probability 0.45 and player B should choose

strategy b1 with probability 0.55.