Transcript
108 ? Test Item File
Chapter Six ? 109
Excel Problems
1. Mr. Smith, an avid reader, must decide on which books to take with him during a long flight. Mr. Smith will use his carryon bag which can hold a maximum of 20 pounds. Mr. Smith has attached a satisfaction index for each book, based on a 5-point scale (1 = low satisfaction, 5 =high satisfaction), as shown below.
Book Satisfaction Index Weight (lbs.)
Marketing 4 4
History 5 3
Statistics 1 3
Management 3 5
Finance 3 4
Economics 2 3
Excel 5 4
Access 4 5
Which books should Mr. Smith take with him on the flight to maximize his satisfaction index?
2. Six products are currently waiting processing on a single machine. The machine is available today for a maximum of 25 hours. The processing time per hour for each product along with the profit contribution per product is show below.
Product Profit Contribution Processing Time (Hours)
A $55 5
B $70 4
C $45 6
D $60 5
E $50 3
F $65 6
Which products should be processed to maximize the total profit contribution?
3. Refer to question 2. Assume that the following conditions must be met:
a) We want to ensure that exactly one of these products: A, B, or C must be processed.
b) We want to ensure that if product E is processed then product F must be processed?
Which products should be processed to maximize the total profit contribution?
4. A decision maker is provided with 5 different potential projects and must determine which projects to choose. The projects require different amounts of capital and different expected net present values (NPV) over the next three years. Determine which set of projects should be selected in order to achieve the maximum net present value if the decision maker has $150,000 available for investment each year.
NVP Capital Required (in $000s)
Project (in $000s) Year 1 Year 2 Year 3
1 140 70 20 25
2 180 85 40 15
3 120 60 20 20
4 80 30 30 15
5 200 50 15 10
5. Refer to problem 4. Determine which set of projects should be selected in order to achieve the maximum net present value if the following two conditions must also be met:
a) If project 1 is selected, then project 2 must be selected, and vice versa.
b) Since projects 4 and 5 require outsourcing various operations, the decision maker wants at most one of these projects to be included in the solution and not both.
6. A company currently has two factories: F1 and F2, and three retail outlets: R1, R2, and R3. The shipping costs per unit along with the monthly capacity and demand requirements are summarized below:
Shipping Cost Per Unit
R1 R2 R3 Supply
F1 $3 $2 $4 100
F2 $1 $3 $5 200
Demand 100 100 200
The firm has decided to build a new factory to expand its productive capacity. The two sites being considered are Philadelphia and Pittsburgh. The estimated shipping costs for the new factories along with their estimated fixed cost and production capacity are summarized below:
R1 R2 R3 Supply Fixed Cost
Philadelphia $2 $4 $3 100 $20,000
Pittsburgh $3 $5 $2 100 $25,000
Which of the new locations will yield the lowest cost in combination with the existing factories and retail outlets?
7. A company produces four products each of which must undergo assembly, inspection, and packaging. The information below summarizes the hours required for each operation by each product, the total hourly capacity for each operation, and the fixed cost incurred by each product if it is produced.
Hours Required
Available
Operation Product 1 Product 2 Product 3 Product 4 Hours
Assembly 3 4 5 4 500
Inspection 2 1 3 2 300
Packaging 1 1 2 2 200
Fixed Cost $1100 $1000 $900 $850
Each unit of product 1 sold will contribute $60 to profit, and each unit of products 2, 3, and 4 contributes $65, $70, and $55, respectively. What is the optimal product mix?
8. A city is reviewing the location of its fire stations. The city is made up of a number of districts, as illustrated below. A fire station can be placed in any district and is able to handle the fires for both its neighborhood and any adjacent neighborhood. The objective is to minimize the number of fire stations used.
9. An investor is considering 7 different stocks: A, B, C, D, E, F, and G. The expected annual return for each stock is provided as follows:
Annual
Stock Return
A 9.5%
B 8.0%
C 7.0%
D 10.0%
E 8.0%
F 9.0%
G 10%
The investor has imposed the following restrictions regarding the composition of the portfolio:
the portfolio must include exactly one of the following stocks: either A or B.
if stock B is selected, then stock F must also be selected.
if stock D is selected, then stock E must be excluded.
Which stocks should be included in the portfolio to maximize annual return?
10. A company is considering producing 8 different products for the upcoming holiday season. The profit contribution per product is illustrated below:
Product Profit ($)
1 10
2 12
3 7
4 15
5 8
6 9
7 13
8 11
The marketing manager has imposed the following restrictions on the production mix:
since products 1, 2, and 3 are electronic gadgets, at least two of these products must be in the production mix..
since products 4 and 5 are kids oriented, the production mix must include no more than one of these products.
if product 7 is included in the mix, then product 8 must be included, and vice versa.
Which products should be included in the mix to maximize profit?
11. A developer wishes to expand an office complex and needs to determine how many small, medium, and large offices to include in the expansion. Each small office requires 400 square feet, each medium office requires 700 square feet, and each large office requires 1200 square feet. The current square footage available for expansion is 35,000 square feet. The developer expects to pay $10,000 for each small office, $20,000 for each medium office, and $35,000 for each large office. The developer wishes to limit his expenditures to $500,000. How many of each type of office should be built if the following goals, stated in no particular order, must be met?
Goal 1: The expansion should include approximately 6 small offices.
Goal 2: The expansion should include approximately 11 medium offices.
Goal 3: The expansion should include approximately 15 large offices.
Goal 4: The expansion should consist of approximately 35,000 square feet.
Goal 5: The expansion should cost approximately $500,000.
12. Consider the following linear programming g problem:
Max: 500A + 700B
Subject to:
2A + 3B ? 35 (assembly hours)
3A + 5B ? 40 (Machine hours)
Reformulate and solve this problem as a goal programming problem if the following goals, stated in no particular order, must be met?
Goal 1: Produce at least 15 units of each product.
Goal 2: Avoid overtime in the assembly and machine departments.
Goal 3: Achieve at least $100,000 in profit.
13. Consider the following linear programming problem:
Max: 500A + 700B
Subject to:
2A + 3B ? 35 (assembly hours)
3A + 5B ? 40 (Machine hours)
Reformulate and solve this problem as a goal programming problem if the following goals, with their associated weights, must be met?
Goal 1: Produce at least 15 units of product A; Weight 15
Goal 2: Produce at least 15 units of product B; Weight 15
Goal 3: Minimize overtime in assembly department; Weight 25
Goal 4: Minimize overtime in machine department; Weight 25
Goal 5: Achieve at least $100,000 in profit; Weight 20
14. Consider the following linear programming g problem:
Max: 500A + 700B
Subject to:
2A + 3B ? 35 (assembly hours)
3A + 5B ? 40 (Machine hours)
Reformulate and solve this problem as a goal programming problem if the following prioritized goals must be met?
Goal Priority
Product at least 15 units of each product P1
Minimize overtime in assembly and machine departments P2
Achieve at least $100,000 in profit P3
15. A marketing manager is considering the following advertising media to promote a new
product.
Type Audience Reached/Ad Cost/Ad Maximum No. of Ads
TV 50,000 $3000 10
Radio 25,000 $1000 15
Newspaper 10,000 $500 30
The marketing manager has established the following goals, stated in no particular order, for the advertising campaign:
Goal 1: Reach at least 500,000 individuals
Goal 2: Limit the total spending to $150,000
Formulate and solve this goal programming problem.
16. A marketing manager is considering the following advertising media to promote a new
product.
Type Audience Reached/Ad Cost/Ad Maximum No. of Ads
TV 50,000 $3000 10
Radio 25,000 $1000 15
Newspaper 10,000 $500 30
The marketing manager has established the following goals and weights:
Goal 1: Reach at least 500,000 individuals; Weight 40
Goal 2: Limit the total spending to $150,000; Weight 60
Formulate and solve this goal programming problem.
17. Set up and solve the following nonlinear programming problem using Excel:
Max: 10X1 + 15X2 + 5X3 + 2X33
Subject to
X1 + X2 + X3 ? 50
2X1 + 3X2 ? 150
X1, X2, X3? 0
18. Set up and solve the following nonlinear programming problem using Excel:
Max: X1 + 2X2 + 3X1X2 + 5X33
Subject to
X1 + X2 + X3 ? 75
X1 + X2 ? 15
2X1 + 2X3 ? 40
X1, X2, X3 ? 0
19. Set up and solve the following nonlinear programming problem using Excel:
Max: (X1 – 5)2 + (X2 – 7)2
Subject to
X1 ? 15
X2 ? 15
X1 + X2 ? 10
X1, X2 ? 0
20. Consider the following profit expected from each dollar (Xi) spent in the following advertising media:
Medium Profit
TV 0.0005Xi3
Radio 0.0025Xi2
Newspaper 0.01Xi
How should the advertising budget be allocated if the company wants to spend at least $1000 on each medium without exceeding its $10,000 budget?
