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MNS407 Management Science, Summer 1 2023
407 Week 4: Final (Quiz) INSTRUCTOR
Karen Joiner
National University, La Jolla CA
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QUESTION
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SUN, JUL 30, 2023
11:59 PM MST
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7/11/23, 1:06 AM 407 Week 4: Final - MNS407 Management Science, Summer 1 2023 | WebAssign
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homework, quizzes, and the �nal.
Your last submission is used for your score.
7/11/23, 1:06 AM 407 Week 4: Final - MNS407 Management Science, Summer 1 2023 | WebAssign
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You may need to use the appropriate technology to answer this question.
A project consists of five activities as shown in the following table.
Activity Optimistic Time (hr) Most Probable Time (hr) Pessimistic Time (hr)
Floor sanding 4 5 6
Floor buffing 4 5 6
Paint mixing 0.5 1 1.5
Wall painting 2 3 10
Ceiling painting 3 7.5 9
Naturally, the paint mixing precedes the painting activities. Also, both ceiling painting and floor sanding must be done prior to floor buffing.
(a) Construct the PERT/CPM network for this problem.
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1. [–/1.46 Points] CAMMIMS16 9.TB.059.DETAILS
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(b) What is the expected completion time (in hours) of this project?
hr
(c) What is the probability that the project can be completed within fourteen hours? (Round your answer to four decimal places.)
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A senior MIS design class project team has developed a schedule of activities for their project using their best estimate of completion times as shown in the following table.
Activity Time Immediate Predecessor
A. find client 5
B. write prospectus 3 A
C. obtain approval from client and professor 5 B
D. complete programming 13 C
E. do industry background research 11
F. write final paper 7 D, E
G. write oral report 6 D, E
Both written and oral reports are required. Draw the project network. Can they complete the project in the 45 class days remaining until the end of the semester?
---Select--- , they can complete it in time since the project is expected to be completed in days.
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A grocery store manager must decide how to best present a limited supply of popcorn and soda to its customers. Popcorn can be sold by itself for a profit of $1.40 per tin. Soda can likewise be sold at a profit of $2.40 per liter. To increase appeal to customers, one tin of popcorn and a liter of soda can be packaged together and sold for a profit of $3.30 per bundle. The manager has at most 110 tins of popcorn and 140 liters of soda to make available each day. The manager has decided to stock at least 85 individual tins of popcorn per day (excluding popcorn bundled with soda). Demand for individual liters of soda is at most 130 liters per day (excluding soda bundled with popcorn). The manager wishes to determine how much of each product to stock each day.
Which of the following is the objective function for the grocer's problem? (Let P be the number of individual tins of popcorn stocked each day. Let S be the number of individual sodas stocked each. Let B be the number of bundles stocked. Assume that, within the limitations established by the constraints, the store can sell all the products it stocks.)
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Max 2.4P + 1.4S + 3.3B
Max 1.4P + 2.4S + 3.3B
Min 2.4P + 3.3S + 1.4B
Min 1.4P + 2.4S + 3.3B
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7/11/23, 1:06 AM 407 Week 4: Final - MNS407 Management Science, Summer 1 2023 | WebAssign
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What does sensitivity analysis consider?
how sensitive the decision maker is to risk
how changes in various aspects of the problem affect the recommended decision alternative
how changes in the number of states of nature can impact the recommended decision
None of these are correct.
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Consider the following PERT/CPM network.
From the PERT/CPM network shown in the figure, create a list of activities and their predecessors. (Enter your answers as comma- separated lists. If an activity does not have immediate predecessors, enter NONE.)
Activity Immediate Predecessor
A
B
C
D
E
ℹ
5. [–/1.46 Points] CAMMIMS16 9.TB.048.DETAILS
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F
G
H
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7/11/23, 1:06 AM 407 Week 4: Final - MNS407 Management Science, Summer 1 2023 | WebAssign
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Consider the following table of activities.
Activity Immediate Predecessor
A
B A
C B
D B
E A
F C, D
G E, F
From the schedule of activities shown in the following table, draw the PERT/CPM network.
ℹ
ℹ
6. [–/1.46 Points] CAMMIMS16 9.TB.047.DETAILS
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The point is feasible for the constraint
True
False
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ℹ
(4, 5) 2x + 6x ≤ 30.1 2
7. [–/1.46 Points] ASWMSCI15 2.TB.010.DETAILS
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7/11/23, 1:06 AM 407 Week 4: Final - MNS407 Management Science, Summer 1 2023 | WebAssign
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A firm has 4 plants that produce widgets. Plants A, B, and C can each produce 120 widgets per day. Plant D can produce 60 widgets per day. Each day, the widgets produced in the plants must be shipped to satisfy the demand of 3 customers. Customer 1 requires 95 units per day, customer 2 requires 120 units per day, and customer 3 requires 205 units per day. The shipping costs for each possible route are shown in the table below:
Shipping Costs per unit at Plant Customer 1 Customer 2 Customer 3
A $25 $35 $15
8. [–/1.46 Points] CAMMIMS16 6.TB.045.DETAILS
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B $20 $30 $40
C $15 $20 $25
D $40 $35 $20
The firm needs to satisfy all demand each day but would like to minimize the total costs.
Select the constraint that models customer demand.
x + x + x ≤ 120
x + x + x ≤ 120
x + x + x ≤ 120
x + x + x + x = 95
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B1 B2 B3
C1 C2 C3
A1 A2 A3
A1 B1 C1 D1
7/11/23, 1:06 AM 407 Week 4: Final - MNS407 Management Science, Summer 1 2023 | WebAssign
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Lakewood Fashions must decide how many lots of assorted ski wear to order for its three stores. Information on pricing, sales, and inventory costs has led to the following payoff table, in thousands.
Demand
Order size Low Medium High
1 lot 13 16 16
2 lots 9 24 32
3 lots 6 32 62
(a) Show a regret table.
Demand
Order size Low Medium High Maximum Regret
1 lot
2 lots
3 lots
(b) What decision should be made by the optimist?
1 lot
2 lots
3 lots
(c) What decision should be made by the conservative?
1 lot
2 lots
3 lots
(d) What decision should be made using minimax regret?
1 lot
2 lots
3 lots
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Investment Advisors, Inc., is a brokerage firm that manages stock portfolios for a number of clients. A particular portfolio consists of U shares of U.S. Oil and H shares of Huber Steel. The annual return for U.S. Oil is $3 per share and the annual return for Huber Steel is $5 per share. U.S. Oil sells for $25 per share and Huber Steel sells for $50 per share. The portfolio has $80,000 to be invested. The portfolio risk index (0.50 per share of U.S. Oil and 0.25 per share for Huber Steel) has a maximum of 700. In addition, the portfolio is limited to a maximum of 1,000 shares of U.S. Oil. The linear programming formulation that will maximize the total annual return of the portfolio is as follows.
The computer output is shown below.
Optimal Objective Value = 8400.00000
Variable Value Reduced Cost
U 800.00000 0.00000
H 1200.00000 0.00000
Constraint Slack/Surplus Dual Value
1 0.00000 0.09333
2 0.00000 1.33333
3 200.00000 0.00000
Variable Objective
Coefficient
Allowable
Increase
Allowable
Decrease
U 3.00000 7.00000 0.50000
H 5.00000 1.00000 3.50000
Constraint RHS
Value
Allowable
Increase
Allowable
Decrease
1 80000.00000 60000.00000 15000.00000
2 700.00000 75.00000 300.00000
3 1000.00000 Infinite 200.00000
(a) What is the optimal solution, and what is the value of the total annual return (in $)?
U
H
estimated annual return $
(b) Which constraints are binding? What is your interpretation of these constraints in terms of the problem? (Select all that apply.)
Constraint 1. All funds available are being utilized.
Constraint 2. The maximum permissible risk is being incurred.
Constraint 3. All available shares of U.S. Oil are being purchased.
None of the constraints are binding.
Max 3U + 5H Maximize total annual return s.t.
25U + 50H ≤ 80,000 Funds available 0.50U + 0.25H ≤ 700 Risk maximum
1U ≤ 1,000 U.S. Oil maximum U, H ≥ 0
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(c) What are the dual values for the constraints? Interpret each. (Round your answers to two decimal places.)
constraint 1
Constraint 1 has a slack of $200. Additional dollars added to the available funds will not improve the total annual return.
Constraint 1 has a dual value of 0.09. If an additional dollar is added to the available funds, the total annual return is predicted to increase by $0.09.
Constraint 1 has a dual value of 1.33. If an additional dollar is added to the available funds, the total annual return is predicted to increase by $1.33.
Constraint 1 has a dual value of 3. If an additional dollar is added to the available funds, the total annual return is predicted to increase by $3.
Constraint 1 has a dual value of 5. If an additional dollar is added to the available funds, the total annual return is predicted to increase by $5.
constraint 2
Constraint 2 has a slack of 200. Allowing additional risk will not improve the total annual return.
Constraint 2 has a dual value of 0.09. If the risk index is increased by 1, the total annual return is predicted to increase by $0.09.
Constraint 2 has a dual value of 1.33. If the risk index is increased by 1, the total annual return is predicted to increase by $1.33.
Constraint 2 has a dual value of 3. If the risk index is increased by 1, the total annual return is predicted to increase by $3.
Constraint 2 has a dual value of 5. If the risk index is increased by 1, the total annual return is predicted to increase by $5.
constraint 3
Constraint 3 has a slack of 200 shares. Raising the maximum number of shares of U.S. Oil will not improve the total annual return.
Constraint 3 has a dual value of 0.09. If the maximum number of shares of U.S. Oil is increased by 1, the total annual return is predicted to increase by $0.09.
Constraint 3 has a dual value of 1.33. If the maximum number of shares of U.S. Oil is increased by 1, the total annual return is predicted to increase by $1.33.
Constraint 3 has a dual value of 3. If the maximum number of shares of U.S. Oil is increased by 1, the total annual return is predicted to increase by $3.
Constraint 3 has a dual value of 5. If the maximum number of shares of U.S. Oil is increased by 1, the total annual return is predicted to increase by $5.
(d) Would it be beneficial to increase the maximum amount invested in U.S. Oil? Why or why not?
Yes, each additional share increases the profit by $1.33.
Yes, each additional share increases the profit by $0.09.
Yes, each additional share increases the profit by $200.00.
No, increasing the maximum shares does not affect the optimal value.
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In the following linear programming problem, how much would you be willing to pay for an additional 8 units of Resource W? (Note: This problem requires Solver.)
0
26.25
30
33.75
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Maximize P = 3x + 15y Subject to:
2x + 4y≤12(Resource W) 5x + 2y≤10(Resource Z) x, y ≥ 0
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Consider the following linear programming problem:
(a) Use a graph to show each constraint and the feasible region.
Max 7X + 6Y s.t.
18X + 5Y ≤ 90 12X + 6Y ≤ 72
X + Y ≤ 9 X, Y ≥ 0
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ℹ
12. [–/1.46 Points] CAMMIMS16 2.TB.045.DETAILS
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(b) Identify the optimal solution point on your graph. What are the values of X and Y at the optimal solution?
(c) What is the optimal value of the objective function?
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ℹ
ℹ
(X, Y) =
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Draw the network for this transportation problem. (Let x represent the flow from node i to node j.)ij
Min 2x + 4x + 6x + 10x + 11x + 11x13 14 15 23 24 25 s.t.
x + x + x ≤ 500 x + x + x ≤ 400
x + x = 300 x + x = 300 x + x = 300
x ≥ 0
13 14 15
23 24 25
13 23
14 24
15 25
ij
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ℹ
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ℹ
ℹ
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An LP model for a marketing research application uses the variable HD to represent the number of homeowners interviewed during the day. The objective function minimizes the cost of interviewing this and other categories. There is a constraint that The solution indicates that interviewing another homeowner during the day will increase costs by $5.00. What does this tell you about the HD variable?
The objective function coefficient of HD is 5.
The objective function coefficient of HD is −5.
The dual price for the HD constraint is 5.
The dual price for the HD constraint is −5.
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The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature.
Decision Alternative
States of Nature
230 80 5
80 80 55
Suppose that the decision maker obtained the probabilities and Use the expected value approach to determine the optimal decision.
EV(d ) =
EV(d ) =
The optimal decision is ? .
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HD ≥ 120.
s1 s2 s3
d1
d2
P(s ) = 0.65, P(s ) = 0.15,1 2 P(s ) = 0.20.3
1
2
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