ISDS 361BTest 2

Dr. Chen SAMPLE Spring 2009

INSTRUCTIONS:

  1. There are 20 multiple questions on the test.
  1. Data file (DATA-2SAMPLE.XLS) is in the LANSCHOOL folder of you Drive C:
  1. Fill in your section number, last name, first name and station number on the STUDENT worksheet of DATA-2SAMPLE.XLS before you start.
  1. Use DATA-2SAMPLE.XLS as your calculation spreadsheet. I will collect DATA-2SAMPLE.XLS at the end of test for reference.
  1. Mark your answer on scantron (882) as soon as you finish one problem.
  1. Turn in test questions and scantron at the end of test.
  1. University policy for academic dishonesty is to be strictly followed.

SELECT THE BEST ANSWER

  1. The functional constraints of a linear model with nonnegative variables are 2X1 + 4X2  12 and 4X1 + X2  10. Which of the following points could not be a feasible solution for the model?
  1. X1 = 1, X2 = 2.5
  2. X1 = 0, X2 = 3
  3. X1 = 2, X2 = 2
  4. X1 = 2.25, X2 = 2
  5. None of the above
  1. Squire Leathers produces two styles of women jackets from cowhide. The first requires 70 minutes of labor time and the second requires 100 minutes. The company has 500hours of labor time available each week. Part of the model is:
  1. 70X1 + 100X2 30,000
  2. 70X1 + 100X2 = 30,000
  3. 70X1 + 100X2 30,000
  4. 70X1 30,000and 100X2 30,000
  5. None of the above
  1. Which of the following is true when using summation variables?
  1. The number of constraints will stay the same as in a formulation without the use of summation variables.
  2. The number of variables will stay the same as in a formulation without the use of summation variables.
  3. There are typically fewer non-zero input coefficients on the left side of the constraints.
  4. Percentage constraints cannot be formulated without the use of summation variables.
  5. None of the above.
  1. Review the Excel spreadsheet below.

Based on the information in the spreadsheet, we can conclude:

  1. There may be alternate optimal solutions.
  2. The range of feasibility for Hours Used Electrical is unlimited.
  3. For every extra unit of Hours Used Gas, the objective function value will increase by 80.
  4. The range of optimality for House Inspections is 25 to 29.
  5. None of the above
  1. iTradehas $100,000 to invest in five stocks and two bonds. X1, X2, X3, X4 and X5 denote the amounts invested in each of the stocks, and Y1and Y2 equal the amounts invested in each of the two bonds. Which of the following shows that at least 30% of the investment in stocks must be in stock 1?
  1. X1 30,000
  2. X1 - .3X2 -.3X3 - .3X4 -.3X5 0
  3. X1  .4(X2 + X3 + X4 +X5 +Y1 + Y2)
  4. .7X1 - .3X2 - .3X3 - .3X4 -.3X5 0
  5. None of the above
  1. Given the linear programming model:

Min.5X1 + 3X2

S.T.8X1 + 6X2  10000

-5X1 + 2X2  12000

X1 + 2X2  1000

X1, X2>= 0

(Excel input is on Worksheet 6)

  1. Unbounded
  2. X1 = 0 / X2 = 6000 / Objective Function Value = 18000
  3. X1 = 1000/ X2 = 0 / Objective Function Value = 5000
  4. X1 = 2400 / X2 = 0 / Objective Function Value = 12000
  5. None of the above.

[Red Star Bike] A small manufacturer of bicycle makes three models of road bikes:

  • Bike frame is made of a special FormularOne composite.
  • Each bike requires 2 tires.
  • Components, such as handles, brake and seat required to assemble the bike are in abundant supply and will not affect production.
  • Each week it can assign up to 6 workers working 8 hours per day, 5 days a week for production – sunk cost.
  • Each week it can purchase up to
  • 2400 ft. of FormularOneComposites for frame for $2.50 per ft.
  • 450tires for $12 each.
  • Other production and marketing information is as follows:

  • Calculation of per unit profit for the three product results as follows:

A Linear Programming Model is formulated as follows:

DECISION VARIABLES

X1:Number of RD-1 bikes produced weekly

X2:Number of RD-2 bikes produced weekly

X3:Number of RD-3 bikes produced weekly

OBJECTIVE FUNCTION

Max: 66X1 + 116X2 + 101X3

CONSTRAINTS

10X1 + 12X2 + 14X3<= 2400 (FormularOne Composite)

2X1 + 2X2 + 2X3<= 450 (Tires)

50X1 +120X2 +100X3<= 14400 (Production time)

NON-NEGATIVITY

X1, X2, X3 >= 0

Model is input into Excel and Solver is called to solve the LP. Below is the sensitivity report of the Solver solution: (see Worksheet 7)

  1. [Red Stare Bike] The optimal total profit is:
  1. $17,027.86
  2. $10,908
  3. $17,100
  4. $17,250
  5. None of the above
  1. [Red Stare Bike]If extra 10 tires are available, what are you willing to pay for them?
  1. $151.4
  2. $210
  3. $271.4
  4. $450
  5. None of the above
  1. [Red Stare Bike]If a half-time worker could be added to the labor force,what is the most we would be willing to pay him?
  1. $1,500
  2. $2,100
  3. $3,050.28
  4. $857.14
  5. None of the above
  1. [Red Stare Bike]If an additional full-time worker were added,what is the most we would be willing to pay him?
  1. $1,500
  2. $1,714.29
  3. The problem is infeasible because change is outside range of feasibility.
  4. Has to re-solve the LP to determine the value of additional full-time worker.
  5. None of the above
  1. [Red Stare Bike]Current selling price of RD-3 is $250, what is the minimum selling price for the RD-3 model that would justify its production?
  1. $100.29
  2. $101.71
  3. $249.29
  4. $250.71
  5. None of the above
  1. [Red Stare Bike]Within what range of values for the net profit of RD-2’swill the optimal solution remains the same?
  1. [1 to 42.4]
  2. [115 to 158.4]
  3. [117.6 to 221]
  4. [219 to 226.4]
  5. None of the above
  1. The probabilistic approach characterized by PERT does not use:
  1. Optimistic activity times.
  2. Median activity times.
  3. Pessimistic activity times.
  4. Most likely activity times.
  5. None of the above

[Webb Inc.]Considerthe following activity schedule table (SeeWorksheet 14) for a maintenance project of Webb Inc. (time in weeks):

  1. [Webb Inc.] What is slack time of activity D?
  2. 4 weeks
  3. 6 weeks
  4. 8 weeks
  5. 12 weeks
  6. None of the above
  1. [Webb Inc.] The earliest project completion time is?
  2. 17 weeks
  3. 18 weeks
  4. 19 weeks
  5. 21 weeks
  6. None of the above

  1. Consider the following payoff table in which D1 through D4 represent decisions, S1 through S4 represent states of nature, and the values in the cells represent profits.(SeeWorksheet 16)

S1 / S2 / S3 / S4
D1 / -20 / 40 / 60 / 100
D2 / 30 / 120 / 60 / -50
D3 / 30 / 30 / 40 / 40
D4 / 10 / -60 / 80 / 70

The optimal decision under the maximax criterion is:

  1. D1
  2. D2
  3. D3
  4. D4
  5. Cannot determine with information given
  1. Consider the following payoff table in which D1 through D4 represent decisions, S1 through S4 represent states of nature, and the values in the cells represent profits.(SeeWorksheet 17)

S1 / S2 / S3 / S4
D1 / 30 / 20 / -50 / 100
D2 / 60 / 120 / 40 / -80
D3 / 20 / 0 / 60 / 80
D4 / 40 / -60 / 80 / 80

Suppose that each state of nature is equally likely to occur. The expected value of perfect information is:

  1. 0
  2. 40
  3. 50
  4. 90
  5. None of the above
  1. Consider a decision making problem with three states of nature: S1, S2, and S3, for which P(S1) = .1 and P(S2) = .3. Suppose also that there are two possible sample indicators, I1 and I2, and the following conditional probabilities hold:

P(I1|S1) = .2

P(I1|S2) = .4

P(I1|S3) = .6.

(SeeWorksheet 18)

What is the Posterior Probability P(S2|I2)?

  1. .18
  2. .24
  3. .36
  4. .50
  5. None of the above
  1. Consider the following information for the activities comprising a small construction project which is scheduled to complete in 26 days. (Costs are in $1000’s.)(SeeWorksheet 19)

Normal Schedule / Crash Schedule
Activity / Slack / Time / Cost / Time / Cost
M / 0 / 7 / 10 / 4 / 19
N / 2 / 5 / 6 / 5 / 6
O / 0 / 4 / 7 / 2 / 12
P / 0 / 5 / 9 / 3 / 13
Q / 2 / 2 / 5 / 1 / 6
R / 0 / 4 / 9 / 4 / 9
S / 0 / 6 / 12 / 5 / 15

If the project must be completed in 25 days, which activity should be accelerated?

  1. Activity N
  2. Activity O
  3. Activity P
  4. Activity Q
  5. None of the above
  1. In a PERT network, you are given the following data with times in weeks. (See Worksheet 20)

What is the probability the project will be completed within one year (52 weeks)?

Activity / Optimistic Time
a / Most Likely Time
m / Pessimistic Time
b / Immediate Predecessors
A / 9 / 11 / 13 / --
B / 4 / 9 / 20 / --
C / 2 / 11 / 14 / A
D / 5 / 6 / 13 / A, B
E / 3 / 6 / 11 / D
F / 9 / 10 / 11 / C, D
G / 7 / 20 / 21 / E, F
  1. 0.1714
  2. 0.3162
  3. 0.5000
  4. 0.8286
  5. None of the above

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