Develop a capital budgeting problem to maximize the total net present value in this situation.

 

  1. A logistics specialist for Charm City Inc. must distribute cases of parts from 3 factories to 3 assembly plants. The monthly supplies and demands, along with the per-case transportation costs are:

 

Assembly Plant

 

1                      2                      3                      Supply

 

__________________________________________________________________

 

A         6                      10                    14                    200

 

Factory                        B          2                      2                      6                      400

 

C          2                      8                      7                      200

 

__________________________________________________________________

 

Demand                       220                  320                  200

 

 

 

The specialist wants to distribute at least 100 cases of parts from factory B to assembly plant 2.

 

 

 

(a) Formulate a linear programming problem to minimize total cost for this transportation problem.

 

(b) Solve the linear programming formulation from part (a) by using either Excel or QM for Windows. Find and interpret the optimal solution and optimal value. Please also include the computer output with your submission.

 

 

 

The following questions are mathematical modeling questions. Please answer by defining decision variables, objective function, and all the constraints. Write all details of the formulation. Please do NOT solve the problems after formulating.

 

 

 

  1. A congressman’s district has recently been allocated $45 million for projects. The congressman has decided to allocate the money to four ongoing projects. However, the congressman wants to allocate the money in a way that will gain him the most votes in the upcoming election. The details of the four projects and votes per dollar for each project are given below.

 

 

 

Project             Votes/dollar

 

________________________

 

Parks                     0.07

 

Education               0.08

 

Roads                     0.09

 

Health Care           0.11

 

Family Welfare     0.08

 

 

 

In order to also satisfy some local influential citizens, he must meet the following guidelines.

 

– None of the projects can receive more than 30% of the total allocation.

 

– The amount allocated to education cannot exceed the amount allocated to health care.

 

– The amount allocated to roads must be equal to or more than the amount spent on parks.

 

– All of the money must be allocated.

 

 

 

Formulate a linear programming model for the above situation by determining

 

(a) The decision variables

 

(b) Determine the objective function. What does it represent?

 

(c) Determine all the constraints. Briefly describe what each constraint represents.

 

 

 

Note: Do NOT solve the problem after formulating.

 

 

 

  1. An ad campaign for a trip to Greece will be conducted in a limited geographical area and can use TV time, radio time, newspaper ads, and magazine ads. Information about each medium is shown below.

 

Medium Cost Per Ad Number Reached
TV 8500 12000
Radio 1800 4000
Newspaper 2400 5500
Magazine 2200 4500

 

 

 

The number of TV ads cannot be more than 4. Each of the media must have at least two ads. The total number of Magazine ads and Newspaper ads must be more than the total number of Radio ads and TV ads. There must be at least a total of 12 ads. The advertising budget is $50,000. The objective is to maximize the total number reached.

 

 

 

Formulate a linear programming model for the above situation by determining

 

(a) The decision variables

 

(b) Determine the objective function. What does it represent?

 

(c) Determine all the constraints. Briefly describe what each constraint represents.

 

 

 

Note: Do NOT solve the problem after formulating.

 

 

 

  1. The Charm City Vacuum Company wants to assign three salespersons to three sales regions. Given their experiences, the salespersons are able to cover the regions in different amounts of time. The amount of time (days) required by each salesperson to cover each region is shown in the following table:

 

                                          Region (days)

 

Salesperson                 I           II            III

 

________________________________________

 

A                           11          18           12

 

B                          11           15           14

 

C                           10           14           16

 

 

 

However, because of his health reason, salesperson C does not want to be assigned to region II.

 

The Company wants to assign either salesperson A or salesperson C to region I. The objective is to minimize total time of covering the three sales regions.

 

 

 

(a) The decision variables

 

(b) Determine the objective function. What does it represent?

 

(c) Determine all the constraints. Briefly describe what each constraint represents.

 

 

 

 

 

  1. The Charm City Inc. must select among a series of new investment alternatives. The potential investment alternatives, the net present value of the future stream of returns, the capital requirements, and the available capital funds over the next three years are given below:

 

 

 

Net Present      Capital Requirements ($)

 

Alternative                                  Value ($)      Year 1   Year 2   Year 3

 

_____________________________________________________________

 

Warehouse expansion               30,850          32,000              12,000     38,000

 

Test market new product            92,300          58,000              41,000     45,000

 

Advertising campaign                 40,000          25,000              12,500     11,800

 

Research & Development           82,000          53,000 13,000     44,000

 

Purchase new equipment            33,000          12,500                4,500       8,900

 

_____________________________________________________________

 

Capital funds available                                               110,500            65,000                88,750

 

 

 

The company wants to select at least 3 alternatives. In addition, the company also wants to select at least two alternatives from the warehouse expansion, research & development and purchase new equipment alternatives.

 

 

 

Develop a capital budgeting problem to maximize the total net present value in this situation.

 

 

 

Please answer by defining decision variables, objective function, and all the constraints. Write all details of the formulation. Please do NOT solve the problem after formulating.

 

 

 

 

 

  1. Jodi wants to lease a new car and start a part time business to give people car rides. She has contacted three automobile dealers for pricing information. Each dealer offered Jodi a closed-end 36-month lease with no down payment due at the time of signing. Each lease includes a monthly charge and a mileage allowance. Additional miles receive a surcharge on a per-mile basis. The three dealers provided the details about the monthly lease cost, the mileage allowance, and the cost for additional miles.

 

 

 

Jodi is not sure how many miles she will drive over the next three years for this business but she believes it is reasonable to assume that she will drive 10,000 miles per year, 14,000 miles per year, or 18,000 miles per year. With this assumption, Jodi estimated her total profit for the three lease options. The three lease options and the associated profits for each are given below:

 

 

 

Dealer         10000 Miles             14000 Miles     18000 Miles

 

A               $ 7000                 $10500             $13500

 

B                $ 8500                  $11500             $11000

 

C                 $10000                $ 9500              $ 9800

 

 

 

 

 

Determine the optimal decision to lease the car from a dealer and the profit associated with it by using the following decision criteria.

 

  1. Maximax

 

  1. Maximin

 

  1. Equal likelihood

 

  1. Minimax regret criterion.

 

 

 

  1. For the problem given in Question 2, the probabilities are given by P(10000 miles) = 0.5, P(14000 miles) = 0.3 and P(18000 miles) = 0.2.

 

 

 

  1. Compute the expected value for each decision and select the best one.

 

  1. Compute the expected regret value for each decision and select the best one.

 

  1. Calculate and interpret the expected value of perfect information.

 

 

 

 

 

  1. For each of the following queuing systems, indicate whether it is a single- or multiple-server model, the queue discipline, and whether its calling population is infinite or finite.

 

 

 

 

 

 

 

  1. Hair salon

 

 

 

  1. Bank

 

 

 

  1. Laundromat

 

 

 

  1. Doctor’s office

 

 

 

  1. Adviser’s office

 

 

 

  1. Airport runway

 

 

 

  1. Service station

 

 

 

  1. Explain and provide example – The Single-Server Waiting Line

 

 

 

  1. What are the different types of simulation models?
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