Explain how the applications of integer programming differ from those of linear programming.
Integer programming is concerned with optimization problems in which some of the variables are required to take on discrete values. Rather than allow a variable to assume all real values in a given range, only predetermined discrete values within the range are permitted. In most cases, these values are the integers, giving rise to the name of this class of models. Models with integer variables are very useful. Situations that cannot be modeled by linear programming are easily handled by integer programming. Primary among these involve binary decisions such as yes-no, build-no build or invest-not invest. Although one can model a binary decision in linear programming with a variable that ranges between 0 and 1, there is nothing that keeps the solution from obtaining a fractional value such as 0.5, hardly acceptable to a decision maker. Integer programming requires such a variable to be either 0 or 1, but not in-between. Unfortunately integer programming models of practical size are often very difficult or impossible to solve. Linear programming methods can solve problems orders of magnitude larger than integer programming methods. A typical mathematical program consists of a single objective function, representing either a profit to be maximized or a cost to be minimized, and a set of constraints that circumscribe the decision variables. In the case of a linear program (LP) the objective function and constraints are all linear functions of the decision variables. At first glance these restrictions would seem to limit the scope of the LP model, but this is hardly the case. Because of its simplicity, software has been developed that is capable of solving problems containing millions of variables and tens of thousands of constraints. Why is “rounding-down” an LP solution a suboptimal way to solve integer programming problems?

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MAT540Week 6 Homework
Complete the following problems from Chapter 2:
1. Problems 2, 6, 7, 12, 16, 20
2. Chapter 2
2. A company produces two products that are processed on two assembly lines. Assembly line 1 has 100 available hours, and assembly line 2 has 42 available hours. Each product requires 10 hours of processing time on line 1, while on line 2 product 1 requires 7 hours and product 2 requires 3 hours. The profit for product 1 is $6 per unit, and the profit for product 2 is $4 per unit.
a. Formulate a linear programming model for this problem.
b. Solve the model by using graphical analysis.
6. The Pinewood Furniture Company produces chairs and tables from two resources – labor and wood. The company has 80 hours of labor and 36 board-ft. of wood available each day. Demand for chairs is limited to 6 per day. Each chair requires 8 hours of labor and 2 board-ft. of wood, whereas a table requires 10 hours of labor and 6 board-ft. of wood. The profit derived from each chair is $400 and from each table, $100. The company wants to determine the number of chairs and tables to produce each day in order to maximize profit. Formulate a linear programming model for this problem.
a. Formulate a linear programming model for this problem.
b. Solve the model by using graphical analysis.
7. In Problem 6, how much labor and wood will be unused if the...

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MAT540Week 4 Homework
Chapter 15 problems
2. The manager of the Carpet City outlet needs to make an accurate forecast of the demand for SoftShag carpet (its biggest seller).If the manager does not order enough carpet from the carpet mill,customers will buy their carpet from one of Carpet City’s many competitors. The manager has collected the following demand data for the past 8 months:
Month Demand for Soft Shag Carpet (1,000 yd.)
1 8
2 12
3 7
4 9
5 15
6 11
7 10
8 12
a. Compute a 3-month moving average forecast for months 4 through 9.
b. Compute a weighted 3-month moving average forecast for months 4 through 9. Assign weights of 0.55,0.33,and 0.12 to the months in sequence, starting with the most recent month.
c. Compare the two forecasts by using MAD. Which forecast appears to be more accurate?
6. The manager of the Petroco Service Station wants to forecast the demand for unleaded gasoline nextmonth so that the proper number ofgallons can be ordered from the distributor.The owner has accumulated the following data on demand for unleaded gasoline from sales during the past 10 months:
Month Gasoline Demanded (gal.)
October 800
November 725
December 630
January 500
February 645
March 690
April 730
May 810
June 1,200
July 980
a. Compute an exponentially...

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MAT540WEEK 1 TO 11(Strayer)
MAT540 Week 1 Homework
Chapter 1, Problems 2, 4, 12, 14, 20, 22
2. The Retread Tire Company recaps tires. The fixed annual cost of the recapping operation is $60,000.The variable cost of recapping a tire is $9.The company charges $25 to recap a tire.
a. For an annual volume of 12,000 tires, determine the total cost, total revenue, and profit.
b. Determine the annual break-even volume for the Retread Tire Company operation.
4. Evergreen Fertilizer Company produces fertilizer. The company’s fixed monthly cost is $25,000, and its variable cost per pound of fertilizer is $0.15. Evergreen sells the fertilizer for $0.40 per pound. Determine the monthly break-even volume for the company.
12. If Evergreen Fertilizer Company in Problem 4 changes the price of its fertilizer from $0.40 per pound to $0.60 per pound, what effect will the change have on the break-even volume?
14. If Evergreen Fertilizer Company increases its advertising expenditures by $14,000 per year, what effect will the increase have on the break-even volume computed in Problem 13?
Reference Problem 13: If Evergreen Fertilizer Company changes its production process to add a weed killer to the fertilizer in order to increase sales, the variable cost per pound will increase from $0.15 to $0.22. What effect will this change have on the break-even volume computed in Problem 12?
20....

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MAT540Week 2 Quiz
Question 1
If variable costs increase, but price and fixed costs are held constant, the break even point will decrease.
Question 2
Parameters are known, constant values that are usually coefficients of variables in equations.
Question 3
Probabilistic techniques assume that no uncertainty exists in model parameters.
Question 4
In general, an increase in price increases the break even point if all costs are held constant.
Question 5
P(A | B) is the probability of event A, if we already know that event B has occurred.
Question 6
A continuous random variable may assume only integer values within a given interval.
Question 7
The events in an experiment are mutually exclusive if only one can occur at a time.
Question 8
A bed and breakfast breaks even every month if they book 30 rooms over the course of a month. Their fixed cost is $4200 per month and the revenue they receive from each booked room is $180. What their variable cost per occupied room?
Question 9
The indicator that results in total revenues being equal to total cost is called the
Question 10
If the price increases but fixed and variable costs do not change, the break even point
Question 11
A university is planning a seminar. It costs $3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $25 per student for the administrators to provide the course materials. If...

...TQuantitative Methods – MAT540 Student Course Guide Prerequisite: MAT 300 Quarter Meeting Days/Time Instructor Instructor Phone Instructor E-mail Instructor Office Hours/Location Academic Office Phone Number Strayer Technical Support INSTRUCTIONAL MATERIAL – Required
( including all mandatory software)
1-877-642-2999
Taylor, B. M. (2010). Introduction to management science (10th ed.). Upper Saddle River, NJ: Pearson/Prentice Hall. QM for Windows and Treeplan add-on for Excel. This software is available in the Open Lab at Strayer campuses, and can also be downloaded from the textbook's companion website.
http://wps.prenhall.com/bp_taylor_introms_10/112/28870/7390751.cw/index.html
Scientific Calculator INSTRUCTIONAL MATERIAL - Supporting The following resources provide additional background and supporting information for this course. There is no need to purchase these items for the course.
Buglear, J. (2005) Quantitative methods for business: the A to Z. Oxford, U.K.: Elsevier Butterworth-Heinemann. Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., Martin, R. K. (2010) Quantitative methods for business. (11th Ed.) Mason, OH: South-western (Cengage). http://www.msubillings.edu/BusinessFaculty/Harris/LP_Problem_intro.htm Dilgard, L. A. (2009, Summer) Worst forecasting practices in corporate America and their solutions -- case studies. Journal of Business Forecasting, 28 (2), 4 - 13. Retrieved from EBSCO-Host...

...Final Examination
Math 540 Quantitative Methods
Good luck on the exam. I hope you have enjoyed the course. Dr. West
Multiple Choice (2 points each) (Select 8 – drop 1)
______1) For your project, what one way will not possibly generate increased profit?
a) Increase your building space or lot size.
b) Decrease the money paid to employees.
c) Refinance the loan at a lower rate.
d) Charge more for your services.
_____ 2) Which of the following is a valid objective function in linear programming?
a) Max 5xy.
b) Min 4x + 5y - (2/3)z.
c) Max 4 x 2 + 6 Y 2.
d) Min (x + y) / z.
e) None of the above.
______3) The improvement in the value of the objective function per unit increase in a right-hand side is the
a. sensitivity value.
b. shadow price.
c. constraint coefficient.
d. slack value.
_____4) Study of how changes in the coefficients of a linear programming problem affect the optimal solution is called
a. sensitivity analysis.
b. transshipment analysis.
c. sunk cost analysis.
d. duality analysis.
e. none of the above.
_____5) Which of these is not a type of integer model?
a. a real integer...

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MAT540WEEK 1 TO 11(Strayer)
MAT540 Week 1 Homework
Chapter 1, Problems 2, 4, 12, 14, 20, 22
2. The Retread Tire Company recaps tires. The fixed annual cost of the recapping operation is $60,000.The variable cost of recapping a tire is $9.The company charges $25 to recap a tire.
a. For an annual volume of 12,000 tires, determine the total cost, total revenue, and profit.
b. Determine the annual break-even volume for the Retread Tire Company operation.
4. Evergreen Fertilizer Company produces fertilizer. The company’s fixed monthly cost is $25,000, and its variable cost per pound of fertilizer is $0.15. Evergreen sells the fertilizer for $0.40 per pound. Determine the monthly break-even volume for the company.
12. If Evergreen Fertilizer Company in Problem 4 changes the price of its fertilizer from $0.40 per pound to $0.60 per pound, what effect will the change have on the break-even volume?
14. If Evergreen Fertilizer Company increases its advertising expenditures by $14,000 per year, what effect will the increase have on the break-even volume computed in Problem 13?
Reference Problem 13: If Evergreen Fertilizer Company changes its production process to add a weed killer to the fertilizer in order to increase sales, the variable cost per pound will increase from $0.15 to $0.22. What effect will this change have on the break-even volume computed in Problem 12?
20....

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MAT540 MIDTERM EXAM
1. Deterministic techniques assume that no uncertainty exists in model parameters.
2. A continuous random variable may assume only integer values within a given interval.
3. A joint probability is the probability that two or more events that are mutually exclusive can occur simultaneously.
4. A decision tree is a diagram consisting of circles decision nodes, square probability nodes, and branches.
5. A table of random numbers must be normally distributed and efficiently generated.
6. Starting conditions have no impact on the validity of a simulation model.
7. The Delphi develops a consensus forecast about what will occur in the future.
8. Qualitative methods are the least common type of forecasting method for the long-term strategic planning process.
9. Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot. Assume also that this time is normally distributed with a standard deviation of 2 minutes. What time is exceeded by approximately 75% of the college students when trying to find a parking spot in the main parking lot?
10. __________ is a measure of dispersion of random variable values about the expected value.
11. The __________ is the maximum amount a decision maker would pay for additional information.
12. Developing the cumulative probability distribution helps to determine...