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Linear Programming Problem

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(excel spreadsheet w/ problem attached)

The stock brokerage firm of Blank, Leibowitz, and Weinberger has analyzed and recommended two stocks to an investors’ club of college professors. The professors were interested in factors such as short-term growth, intermediate growth, and dividend rates. These data on each stock are as follows:

Stock $
Factor Lousiana Gas & Power Trimex Insulation Co.
Short-term growth potential per $ invested 0.36 0.24

Intermediate growth potential (over next 3 yrs), per $ invested 1.67 1.5

Dividend Rate Potential 4% 8%

Each member of the club has an investment goal of (1) an appreciation of no less than $720 in the short term, (2) an appreciation of at least $5,000 in the next three years, and (3) a dividend income of at least $200 per year. What is the smallest investment that a professor can make to meet these three goals?

Linear Programming

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The Jane Deere Company manufactures tractors in Provo, Utah. Jeremiah Goldstein, the production planner, is scheduling tractor production for the next three months. Factors that Mr. Goldstein must consider include sales forecasts, straight-time and overtime labor hours available, labor cost, storage capacity, and carrying costs.

The marketing department has forecast that the number of tractors shipped during the next three months will be 250, 305, and 350. Each tractor requires 100 labor hours to produce. In each month, 29,000 straight-time labor hours will be available, and company policy prohibits overtime hours from exceeding 10% of straight-time hours. Straight-time labor cost rate is $20 per hour, including benefits. The overtime labor cost rate is 150% (time and half) of the straight-time rate. Excess production capacity during a month may be used to produce tractors that will be stored and sold during a later month. However, the amount of storage space can accommodate only 40 tractors. A carrying cost of $600 is charged for each month a tractor is stored (if not shipped during the month it was produced). Currently, no tractors are in storage.

How many tractors should be produced in each month using straight-time and using overtime in order to minimize total labor cost and carrying cost? Sales forecasts, straight-time and overtime labor capacities, and storage capacity must be adhered to. Note that during each month, all Asources@ of tractors must exactly equal Auses@ of tractors

 

Integer Linear Programming

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I’ve been trying to figure out this Managerial Decision Making problem. Please help me out. Thank you!

A power company is considering how to increase its generating capacity to meet expected demand in its growing service area. Currently, the company has 750 megawatts (MW) of generating capacity but projects it will need the following minimum generating capacities in each of the next five years:

Year
_________________________________
1 2 3 4 5
______________________________________________________
Minimum Capacity 780 860 950 1,060 1,180
In Megawatts (MW)

The company can increase its generating capacity by purchasing four different types of generators: 10 MW, 25 MW, 50 MW, and/or 100 MW. The cost of acquiring and installing each of the four types of generators in each of the next five years is summarized in the following table:

Cost of Generators (in $1,000s) in Year
_____________________________________________

Generator Size 1 2 3 4 5 _______________________________________________________________

10 MW $300 $250 $200 $170 $145

25 MW $460 $375 $350 $280 $235

50 MW $670 $558 $465 $380 $320

100 MW $950 $790 $670 $550 $460

a. Formulate a mathematical programming model to determine the least costly way of expanding the companyĆ¢??s generating assets to the minimum required levels.
b. Implement your model in a spreadsheet and solve it.
c. What is the optimal solution?

 

Linear programming

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I have the problem formulated and have the sensitivity report in Excel in the attachment.

max: 1.3 x1 + 1.09 x2 + 1 x3 + 1.09 x4 + 0.75 x5 + 0.865 x6;
x1 >= 10
x2 >= 10
x3 >= 10
x4 >= 10
x5 >= 10
x6 >= 10
-.25×1-.25×2+.75×3+.75×4-.25×5-.25×6<=0
8 x1 + 6 x2 + 7 x3 + 7 x4 + 9 x5 + 9 x6 <= 3000
1 x1 + 1 x2 + 1 x3 + 1 x4 + 0.5 x5 + 0.5 x6 <= 280
3 x1 + 1 x2 + 1 x3 + 1 x4 + 1 x5 + 1 x6 <= 500
1 x1 + 0.5 x2 + 2 x3 + 2 x4 + 1 x5 + 1 x6 <= 300
1 x2 <= 25
0.45 x3 <= 25
0.4 x4 <= 25
1 x5 <= 25
0.75 x6 <= 25

Must linear programming be used under conditions of certainty?

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The production manager of a large Cincinnati manufacturing firm once made the statement, “I would like to use LP, but it’s a technique that operates under conditions of certainty. My plant doesn’t have that certainty; it’s a world of uncertainty. So LP can’t be used here.” Do you think this statement has any merit? Why or why not? Explain why the manager may have said it and then further substantiate his argument or compose a rebuttal.

Objective Function vs. Constraints in a Linear Programming Model

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Under what circumstances is the objective function more important than the constraints in a linear programming model? Under what circumstances are the constraints more important than the objective function in a linear programming model?

Linear Programming Concepts, shadow price and sensitivity

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What does the shadow price reflect in a maximization problem? explain.
How do the graphical and computer-based methods of solving LP problems differ? In what ways are they the same? Under what circumstances would you prefer to use the graphical approach? How does sensitivity analysis affect the decision making process? How could it be used by managers?