ch8 1.
Linear programming assumes that the profit from each activity is proportional to the level of that activity. True False
2.
If the slope of a graph never increases but sometimes decreases as the level of the activity increases, then it is said to have decreasing marginal returns. True False
3.
In problems where the objective is to minimize the total cost of the activities, an activity is said to have decreasing marginal returns if the slope of its cost graph never increases but sometimes decreases as the level of the activity increases. True False
4.
If C1:C6 are all changing cells, then SUMPRODUCT(C1:C3, C4:C6) is a linear function. True False
5.
If C1 is a changing cell, then ROUND(C1) is a linear function. True False
6.
If D1 is a data cell, and C1 and C2 are changing cells, then IF(D1 >= 2, C1, C2) is a linear function. True False
7.
Nonlinear programming problems with decreasing marginal returns are generally easier to solve then nonlinear programming problems with increasing marginal returns. True False
8.
Sometimes the Solver can return different solutions when optimizing a nonlinear programming problem. True False
9.
Excel's curve fitting method is used to graph a nonlinear equation. True False
10. Excel's curve fitting method is used to find the values of the parameters for an equation that best fit data. True False 11. A local maximum is always a global maximum in a nonlinear programming problem. True False 12. A quadratic programming problem is a special type of linear programming problem. True False 13. Having activities with decreasing marginal returns is the only way that the proportionality assumption can be violated. True False 14. Separable programming is applicable when there are increasing or decreasing marginal returns. True False 15. In separable programming, each activity that violates the proportionality assumption is separated into parts with a new variable for each part. True False 16. In some cases of separable programming, the profit graphs will be curves rather than a series of line segments. True False This study source was downloaded by 100000840946462 from CourseHero.com on 02-15-2022 20:58:54 GMT -06:00
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17. When the marginal return from an activity decreases on a continuous basis, the profit graphs will consist of a series of line segments. True False 18. Applying separable programming requires having profit graphs that are smooth curves. True False 19. A nonlinear function may contain a product of two variables. True False 20. In separable programming, if an activity violates the proportionality assumption it must have increasing marginal returns. True False 21. Profit = 3x1 + 2x2 + 9x1x2 is an example of a nonlinear function. True False 22. The additivity assumption of linear programming states that each term in the objective function is the sum of two or more variables. True False 23. The additivity assumption can be violated by nonlinear programming because of cross-product terms involving the product of two variables. True False 24. It now is common practice for professional managers of large stock portfolios to use computer models based partially on separable programming. True False 25. When applying nonlinear programming to portfolio selection, a trade-off is being made between the expected return and the risk associated with the investment. True False 26. The risk for a portfolio is decreased when the particular stocks tend to move up and down together. True False 27. Solver Table can be used for nonlinear programming problems to systematically try a number of different starting points. True False 28. Trying different starting points and picking the best solution will always yield the optimal solution to a nonlinear programming problem. True False 29. Evolutionary Solver uses an algorithm based on genetics, evolution, and survival of the fittest. True False 30. Mutation is the technique used to create the next generation of solutions in the Evolutionary Solver. True False 31. The standard Solver keeps track of a large set of candidate solutions, called the population. True False 32. The members of the population used to create the next generation are picked randomly by the Evolutionary Solver. True False 33. Sometimes Evolutionary Solver will make a random change in a member of the population. True False
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34. Evolutionary Solver is often faster than the standard Solver at solving linear programming problems. True False 35. Two runs of the Evolutionary Solver on the same problem will typically yield the same solution. True False 36. If the data cells are in column D and the changing cells are in column C, which of the following are linear formulas in a spreadsheet? A. SUMPRODUCT(D1:D6, C1:C6) B. SUMPRODUCT(C1:C3, C4:C6) C. SUM(C1:C6) D. All of these. E. a and c only. 37. If the data cells are in column D and the changing cells are in column C, which of the following are not linear formulas in a spreadsheet? A. IF(D1 >= 6, C1, C2) B. ROUND(C3) C. ABS(C3) D. All of these. E. b and c only. 38. When there are decreasing marginal returns: A. the slope of the graph never increases but sometimes decreases. B. the slope of the graph never decreases but sometimes increases. C. the graph always consists of a smooth curve. D. the graph always consists of a series of line segments. E. separable programming should not be used. 39. Decreasing marginal returns violates which assumption of linear programming? A. The proportionality assumption. B. The divisibility assumption. C. The additivity assumption. D. All of these. E. None of these. 40. A linear function may contain which of the following? A. A term that contains a single variable with an exponent of 1. B. A term that contains a single variable with an exponent of 2. C. A term that is a constant times the product of two variables. D. All of these. E. b. and c. only. 41. A nonlinear function may contain which of the following? A. A term that contains a single variable with an exponent of 1. B. A term that contains a single variable with an exponent of 2. C. A term that is a constant times the product of two variables. D. All of these. E. b. and c. only. 42. Which of the following can be part of a nonlinear profit graph? A. Decreasing marginal returns. B. Increasing marginal returns. C. Discontinuities. D. All of these. E. a and b only. This study source was downloaded by 100000840946462 from CourseHero.com on 02-15-2022 20:58:54 GMT -06:00
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43. A nonlinear programming problem may have: A. activities with increasing marginal returns. B. activities with decreasing marginal returns. C. nonlinear functional constraints. D. All of these. E. b. and c. only. 44. Which of the following is an example of a nonlinear function? A. Profit = 5x + 7x – 2x 2. 1
2
2
B. Profit = 8x1x2 – x12 – 4x22. C. Profit = x1 + 6x2 + 3x1x2. D. None of these. E. All of these.
45. The requirement that each term in the objective function only contains a single variable is in a linear program is referred to as: A. the proportionality assumption. B. the divisibility assumption. C. the additivity assumption. D. a nonlinear function. E. None of these. 46. The measure of risk in a portfolio selection problem is called: A. the covariance of the return. B. the variance of the return. C. the expected return. D. decreasing marginal return. E. None of these. 47. The measure of risk for pairs of stocks in a portfolio selection problem is called: A. the covariance of the return. B. the variance of the return. C. the expected return. D. decreasing marginal return. E. None of these. 48. Separable programming will always find the optimal solution when the following is true: A. The profit or cost graph is piecewise linear. B. There are decreasing marginal returns. C. a and b must both be true. D. Separable programming only finds an approximate solution. E. None of these. 49. Which of the following techniques is appropriate when a nonlinear programming problem has multiple local optima? A. Running Solver many times with different starting points. B. Using Solver Table to try different starting points. C. Using Evolutionary Solver. D. All of these. E. b and c only.
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50. Evolutionary Solver is based on which of the following concepts? A. Genetics. B. Evolution. C. Survival of the Fittest. D. All of these. E. b and c only. 51. Evolutionary Solver is best suited to which kinds of problems? A. Linear programs. B. Nonlinear programs with difficult objective functions. C. Nonlinear programs with decreasing marginal returns and no discontinuities. D. Nonlinear programs with many constraints. E. None of these. 52. Which of the following are advantages of the Evolutionary Solver? A. The complexity of the objective function does not matter. B. It will always find the optimal solution. C. It is faster than the standard Solver. D. It always finds the same solution. E. None of these. 53. Which of the following are disadvantages of the Evolutionary Solver? A. It does not deal well with complicated objective functions. B. It does perform well on models with many constraints. C. It is easily trapped at local optima. D. a and b. E. None of these.
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