# Project #52137 - Quantitative Decisions in Business

Chapter 9 Transportation, Assignment, and Network Models

9-1 Is transportation model an example of decision making under certainty or decision making under uncertainty? Why?

9-10 The Saussy Lumber Company ships pine flooring to three buildings from its mills in Pineville, Oak Ridge, and Mapletown. Determine the best transportation schedule for the data given in the table below. Use the northwest corner rule and the stepping-stone method.

9-13 Finnish Furniture manufactures tables in facilities located in three cities- Reno, Denver, and Pittsburgh. The tables are then shipped to three retail stores located in Phoenix, Cleveland, and Chicago. Management wishes to develop a distribution schedule that will meet the demands at the lowest possible cost. The shipping cost per unit from each of the sources to each of the destinations is shown in following table:

From \To Phoenix Cleveland Chicago
Reno 10 16 19
Denver 12 14 13
Pittsburgh 18 12 12

The available supplies are 120 units from Reno, 200 from Denver, and 160 from Pittsburgh. Phoenix has a demand of 140 units, Cleveland has a demand of 160 units, and Chicago has a demand of 180 units. How many units should be shipped from each manufacturing facility to each of the retail stores if the cost is to be minimized? What is the total cost?

9-22 In a job shop operation, four jobs may be performed on any four machines. The hours required for each job on each machine are presented in the following table. The plant supervisor would like to assign jobs so that the total time is minimized. Find the best solution. Which assignments should be made?

JOB Machine W Machine X Machine Y Machine Z

A12 10 14 16 13
A15 12 13 15 12
B2 9 12 12 11
B9 14 16 18 16

9-29 The Patricia Garcia Company is producing seven new medical products. Each of Garcia's eight plants can add one more product to its current line of medical devices. The unit manufacturing costs for producing the different parts at the eight plants are shown in the table above. How should Garcia assign the new products to the plants to minimize manufacturing costs?

MEDICAL PLANT

DEVICES 1 2 3 4 5 6 7 8

C53 \$0.10 \$0.12 \$0.13 \$0.11 \$0.10 \$0.06 \$0.16 \$0.12

C81 0.05 0.06 0.04 0.08 0.04 0.09 0.06 0.06

D5 0.32 0.40 0.31 0.30 0.42 0.35 0.36 0.49

D44 0.17 0.14 0.19 0.15 0.10 0.16 0.19 0.12

E2 0.06 0.07 0.10 0.05 0.08 0.10 0.11 0.05

E35 0.08 0.10 0.12 0.08 0.09 0.10 0.09 0.06

G99 0.55 0.62 0.61 0.70 0.62 0.63 0.65 0.59

Chapter 10 Integer Programming, Goal Programming, and Nonlinear Programming

10-9 Which of the following are NLP problems, and why?

1. Maximize profit = 3X1 + 5X2 + 99X3

Subject to X1 > 10

X2 < 5

X3 > 18

1. Maximize cost = 25X1 + 30X2 + 8X1X2

Subject to X1 > 8

X1 + X2 > 12

0.0005X1 - X2 = 11

1. Maximize Z = P1 d1- + P2d2+ + P3+

Subject to X1 + X2 + d1- - d1 + = 300

X2 + d2- - d2 + = 200

X1 + d3- - d3 + = 100

1. Maximize profit = 3X1 + 4X2

Subject to X1 2 – 5X2 > 8

3X1 + 4X2 > 12

1. Minimize cost = 18X1 + 5X2 + X2 2

Subject to 4X1 – 3X2 > 8

X1 + X2 > 18

Are any of these quadratic programming problems?

10-13 An airline owns an aging fleet of Boeing 737 jet airplanes. It is considering a major purchase of up to 17 new Boeing model 787 and 767 jets. The decision must take into account numerous cost and capability factors, including the following: (10 the airline can finance up to \$1.6 billion in purchases; (2) each Boeing 767 will cost \$110 million; (3) at least one –third of the planes purchased should be the longer- range 787; (4) the annual maintenance budget is to be more than \$8 million; (5) the annual maintenance cost per 787 is estimated to be \$800,000, and it is \$500,000 for each 767purchased; and

(6) each 787 can carry 125,000 passengers per year, whereas each 767 can fly 81,000 passengers annually. Formulate this as an integer programming problem to maximize the annual passenger carrying capability. What category of integer programming problem is this? Solve this problem.

10- 16 Innis Construction Company specializes in building moderately priced homes in Cincinnati, Ohio. Tom Innis has identified eight potential locations to construct new single-family dwellings, but he cannot put up homes on all of the sites because he has only \$300,000 to invest in all projects. The accompanying table shows the cost of constructing homes in each area and the expected profit to be made from the sale of each home. Note that the home-building costs differ considerably due to lot costs, site preparation, and differences in the models to be built.

Note also that a fraction of a home cannot be built.

(a) Formulate Innis's problem using 0-1 integer programming.

(b) Solve with QM for Windows or Excel.

1. The number of people reached should be at least 1,500,000.

1. The total monthly advertising budget should not be exceeded.

1. Together, the number of ads on either TV or radio should be at least 6.

1. No more than 10 ads of any one type of advertising should be used.

1. Formulate this as a goal programming problem.

2. Solve this using computer software.

3. Which goals are exactly met and which of them are not?

10-25 Major Bill Bligh, director of the Army War College’s new 6 month attaché training program, is concerned about how the 20 officers taking the course spend their precious time while in his charge. Major Bligh recognizes that there are 168 hours per week and thinks that his students have been using them rather inefficiently. Bligh lets

X1 = number of hours of sleep needed per week

X2 = number of personal hours (eating, personal hygiene, handling laundry, and so on)

X3 = number of hours of class and studying

X4 = number of hours of social time off base (dating, sports, family visits, and so on)

He thinks that students should study 30 hours a week to have time to absorb material. This is his most important goal. Bligh feels that students need at most 7 hours sleep per night on average and that this goal is number 2. He believes that the goal number 3 is to provide at least 20 hours per week of social time.

1. Formulate this as a goal programming problem.

2. Solve the problem using computer software.

 Subject Mathematics Due By (Pacific Time) 12/21/2014 12:00 pm
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