solve 16 question from Introduction to Management Science, Global Edition THIRTEENTH EDITION Bernard W. Taylor III 13th Edition

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Introduction to Management Science, Global Edition

THIRTEENTH EDITION Bernard W. Taylor III

13th Edition

Chapter 5 2

Question 4 2

Question 8 3

Question 20 4

Question 27 5

Chapter 6 6

Question 4 6

Question 18 7

Question 30 8

Chapter 9 10

Question 3 10

An industrial machinery manufacturer produces shapers and drill presses. The manufacturer fore-casts that the demand for shapers for the next month will be at least 5 and the demand for drill presses for the next month will be at most 7. A shaper earns a profit of €40,000 and a drill press, €50,000. Both the shaper and the drill press use few common components like belts, electric motors, hydraulic drives, sensors, etc. A shaper needs 15 units of such common components and a drill press, 18 units. The store has 200 units of the components in stock. The cost of other parts is allocated from a common budget. A shaper needs €12,000 and a drill press needs €16,000 from the budget. The manufacturer has a budget of €150,000. The manufacturer wants to determine the number of shapers and drill presses to produce to maximize its profits.

a. Formulate an integer programming model for this problem.

b. Solve this model by using the computer.

Samsung sells its four flagship products—cell phones, TVs, computing devices, and memory storage devices—through its exclusive showroom in a city. To support sales, it has hired 20 per-sons and trained them to service every product. Depending on the nature of the job, the cost of overhead expenses varies. The overhead cost of the cellphone section of the showroom per day is £70, for the TV section is £65, for the computing device section is £60, and for the memory storage section is £25. The store has allotted a budget of £1,000 for the showroom per day. A cell phone serviceman generates a revenue of £480 a day, a TV serviceman, £480, a computing devices serviceman, £450, and a memory storage section serviceman, £300. Each section needs at least two servicemen. The outlet wants to determine the number of servicemen to be assigned to each section that will maximize the revenue.

a. Formulate an integer programming model for this problem.

b. Solve this model by using the computer.

The Terraco Motor Company has produced a lightweight, all-terrain vehicle code-named “J99 Terra” for the military. The company is now planning to sell the Terra to the public. It has five plants that manufacture the vehicle and four regional distribution centers. The company is unsure of public demand for the Terra, so it is considering reducing its fixed operating costs by closing one or more plants, even though it would incur an increase in transportation costs. The relevant costs for the problem are provided in the following table. The transportation costs are per thousand vehicles shipped; for example, the cost of shipping 1,000 vehicles from plant 1 to warehouse C is $32,000.

Formulate and solve an integer programming model for this problem to assist the company in determining which plants should remain open and which should be closed and the number of vehicles that should be shipped from each plant to each warehouse to minimize total cost.

Six Sigma is a well-recognized quality management system that employs improvement projects to improve business processes to reduce product and service defects, reduce costs, and increase profits. Each project has a “champion” from upper management who is responsible for the proj-ect’s success. The project leader is known as a “black belt,” and project team members are called “green belts.” Simsun, a manufacturer of cell phone parts and components, has eight improvement projects under consideration, and six champions, 10 black belts, and 25 green belts available to be assigned to the projects. The following table shows for each of the projects the number of green belts required, the percent reduction in defects expected, the cost savings (in $ millions), and the profit improvement (in $ millions).

The company wants to select the projects that will result in the greatest profit improvement while achieving a defect reduction of at least 5 percent and cost savings of at least $6.3 million. Formu-late and solve an integer programming model for this problem.

Steel mills in three cities produce the following amounts of steel:

These mills supply steel to four cities, where manufacturing plants have the following demand:

Shipping costs per ton of steel are as follows:

Because of a truckers’ strike, shipments are prohibited from Birmingham to Chicago.

a. Formulate this problem as a linear programming model, and solve it using the computer.

b. What would be the effect on the optimal solution of a reduction in production capacity at the Gary mill from 320 tons to 290 tons per week?

A private taxi company in the UAE has recently procured 300 taxicabs to meet the rising demands in three cities—Dubai, Abu Dhabi, and Sharjah. Of these taxicabs, 100 are 4-seaters, 100 are 7-seaters, and 100 are 14-seater minivans.

The company has identified the maximum number of taxicabs needed in each city as follows:

The table shows the daily profit in AED for each type of taxicab in each city.

Besides, each city needs at least 20 4-seater taxicabs. Determine how many taxicabs of each type need to be operational in each city to maximize profit.

World Foods, Inc., imports food products such as meats, cheese, and pastries to the United States from warehouses at ports in Hamburg, Marseilles, and Liverpool. Ships from these ports deliver the products to Norfolk, New York, and Savannah, where they are stored in company warehouses before being shipped to distribution centers in Dallas, St. Louis, and Chicago. The products are then distributed to specialty food stores and sold through catalogs. The shipping costs ($/1,000 lb.)

from the European ports to the U.S. cities and the available supplies (1,000 lb.) at the European ports are provided in the following table:

The transportation costs ($/1,000 lb.) from each U.S. city of the three distribution centers and the demands (1,000 lb.) at the distribution centers are as follows:

Determine the optimal shipments between the European ports and the warehouses and the distribution centers to minimize total transportation costs.

The Bay City Parks and Recreation Department has received a federal grant of $600,000 to expand its public recreation facilities. City council representatives have demanded four different types of facilities—gymnasiums, athletic fields, tennis courts, and swimming pools. In fact, the demand by various communities in the city has been for 7 gyms, 10 athletic fields, 8 tennis courts, and 12 swimming pools. Each facility costs a certain amount, requires a certain number of acres, and is expected to be used a certain amount, as follows:

The Parks and Recreation Department has located 50 acres of land for construction (although more land could be located, if necessary). The department has established the following goals, listed in order of their priority:

(1) The department wants to spend the total grant because any amount not spent must be returned to the government.

(2) The department wants the facilities to be used by a total of at least 20,000 people each week.

(3) The department wants to avoid having to secure more than the 50 acres of land already located.

(4) The department would like to meet the demands of the city council for new facilities. How-ever, this goal should be weighted according to the number of people expected to use each facility.

a. Formulate a goal programming model to determine how many of each type of facility should be constructed to best achieve the city’s goals.

b. Solve this model by using the computer so that the solution values are integers.