Introduction to Management Science Midterm Exam October 29, 2002


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1 Answer 25 of the following 30 questions. Introduction to Management Science Midterm Exam October 29, 2002 Graphical Solutions of Linear Programming Models 1. Which of the following is not a necessary assumption for a linear programming function to be used effectively? a. linearity b. certainty c. divisibility d. exponentiality 2. The region which satisfies all of the constraints in a graphical linear programming problem is called the a. region of optimality b. feasible solution space c. region of nonnegativity d. optimal solution space Computer Solution 3. The production manager for the Whoppy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her resources are constraint production time (8 hours = 480 minutes per day) and syrup (1 of her ingredients) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drinks are $3.00 per case and profits for diet soft drinks are $2.00 per case. Which of the following is not a feasible production combination? a. 135R and 120D b. 135R and 0D c. 0R and 120D d. 75R and 90D Sensitivity Analysis 4. In linear programming, sensitivity analysis is associated with (1) objective function coefficient (2) right hand side values of constraints (3) constraint coefficient a. 1 and 2 b. 2 and 3 c. 1 and 3 d. 1, 2 and 3
2 Page 2 A Diet Example 5. Which of the choices below constitutes a simultaneous solution to these equations? 1. 3x + 2y = x + 3y = 12 a. x = 1 / y = 0 b. x = 1 / y = 2 c. x = 2 / y = 0 d. x = 0 / y = 2 A Blend Example 6. A croissant shop produces 2 products: bear claws (B) and almond filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS of almond paste. An almond filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today's production run. Bear claw profits are 20 cents each, and almond filled croissant profits are 30 cents each. What is the almond paste restraint? a. 2B + 4C </= 4800 b. 4B + 2C </= 4800 c. 2B + 3C </= 4800 d. 3B + 1C </= The production manager for Liquor etc. produces 2 kinds of beer: light and dark. Two of his resources are constrained: malt, of which he can get at most 4800 oz per week; and wheat, of which he can get at most 3200 oz per week. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. What is the dark beer constraint? a. 12L + 8D </= 3200 b. 4L + 8D </= 3200 c. 8L + 12D </= 3200 d. 8L + 4D </= 3200 Integer Programming Graphical Solution 8. If the optimal solution to the linear programming relaxation problem is integer, it is the to the integer linear programming. a. real solution b. degenerate solution c. deviate solution d. optimal solution
3 Page 3 The Transportation Model 9. Which of the following are assumptions or requirements of the transportation problem? a. Goods are the same, regardless of source. b. There must be multiple sources. c. Shipping costs per unit do not vary with the quantity shipped. d. all of the above The Shortest Route Problem 10. The first step in the shortest route solution method is to a. select the node with the shortest direct route from the origin b. select any starting node c. arbitrarily select any path in the network from origin to destination d. establish a permanent set with the origin node The Minimal Spanning Tree Problem 11. The first step of the minimal spanning tree solution method is to a. select any starting node b. select the node closest to the starting node to join the spanning tree c. select the closest node not presently in the spanning tree d. make sure all nodes have joined the spanning tree Model Building: BreakEven Analysis 12. There is a fixed cost of $50,000 to start a production process. Once the process has begun, the variable cost per unit is $25. The revenue per unit is projected to be $45. Write an expression for total profit. Graphical Solutions of Linear Programming Models 13. The binding constraints for this problem are the first and second. Min x1 + 2x2 s.t. x1 + x2 >/= 300 2x1 + x2 >/= 400 2x1 + 5x2 </= 750 x1, x2 >/= 0 Keeping c2 fixed at 2, over what range can c1 vary before there is a change in the optimal solution point?
4 Page The binding constraints for this problem are the first and second. Min x1 + 2x2 s.t. x1 + x2 >/= 300 2x1 + x2 >/= 400 2x1 + 5x2 </= 750 x1, x2 >/= 0 If the objective function becomes Min 7x1 + 6x2, what constraints will be binding? Irregular Types of Linear Programming Problems 15. In a linear programming problem, the binding constraints for the optimal solution are: 5x1 + 3x2 </= 30 2x1 + 5x2 </= 20 As long as the slope of the objective function stays between and, the current optimal solution point will remain optimal. Slack Variables 16. Consider the graphical linear programming problem: Max Z = $15x + $20y Subject to: 8x + 5y </= x + y >/= 4 Solve the values for x and y that will maximize revenue. 17. Given the following problem: Max Z = $0.30x + $0.90y a. 2x + 3.2y </= 160 b. 4x + 2y </= 240 c. y </= 40 Solve for the quantities of x and y which will maximize Z. Sensitivity Analysis 18. The production manager for Beer etc. produces 2 kinds of beer: light and dark. Two of his resources are constrained: malt, of which he can get at most 4800 oz per week; and wheat, of which he can get at most 3200 oz per week. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. What is the objective function?
5 Page 5 Integer Programming Problems 19. The production manager for Beer etc. produces 2 kinds of beer: light and dark. Two of his resources are constrained: malt, of which he can get at most 4800 oz per week; and wheat, of which he can get at most 3200 oz per week. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. What is the light beer constraint? Computer Solution of Integer Programming Problems with Excel and QM for Windows 20. Consider a capital budgeting example with 5 projects from which to select. Let xa = 1 if project a is selected, 0 if not, for a = 1, 2, 3, 4, 5. Write the appropriate constraints for each condition. Conditions are independent. No more than 2 of projects 1, 2, and 3 can be chosen. Computer Solution of a Transportation Problem 21. A logistics specialist for Wiethoff Inc. must distribute cases of parts from 3 factories to 3 assembly plants. The monthly supplies and demands, along with the percase transportation costs are: Destination Assembly Plant Supply Source A Factory B C Demand Using the intuitive approach, how many cases of parts should be shipped from factory B to assembly plant 1? The Management Science Approach to Problem Solving 22. Management science can be used in a variety of organizations to solve many different types of problems. 23. A variable is a symbol used to represent an item that can take on any value.
6 Page 6 Sensitivity Analysis 24. Decreasing the objective function coefficient of a variable to its lower limit will create a new problem that has an unbounded solution. Computer Solution 25. Positive shadow prices will never exist in a maximization problem. An Investment Example 26. Standard form requires that fractional relationships between variables be eliminated. A Marketing Example 27. In a balanced model, supply does not equal demand and one set of constraints is </= to the other. Integer Programming Models 28. In a total integer model, all decision variables have integer solution values. Network Components 29. A network is an arrangement of paths connected at various points through which items move. The Minimal Spanning Tree Problem 30. The third step of the minimal spanning tree solution method is to select the node closest to the starting node to join the spanning tree.
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