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Study Resources (Business Management)

40. Solve the following problem graphically. Max 5X + 6Y s.t. 17X + 8Y ≤ 136 3X + 4Y ≤ 36 X, Y ≥ 0 and integer ? a. Graph the constraints for this problem. Indicate all feasible solutions. b. Find the optimal solution to the LP Relaxation. Round down to find a feasible integer solution. Is this solution optimal? c. Find the.
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21. ?Most practical applications of integer linear programming involve only 0 -1 integer variables. a. True b. False 22. ?Integer linear programs are harder to solve than linear programs. a. True b. False 23. Which of the following is the most useful contribution of integer programming? a. finding whole number solutions where fractional solutions would not be.
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21. Inventory a. is held against uncertain usage so that a supply of items is available if needed. b. constitutes a small part of the cost of doing business. c. is not something that can be managed effectively. d. All of the alternatives are correct. 22. Inventory models in which the rate of demand is.
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51. Given the following network with activities and times estimated in days, Activity Optimistic MostProbable Pessimistic A 2 5 6 B 1 3 7 C 6 7 10 D 5 12 14 E 3 4 5 F 8 9 12 G 4 6 8 H 3 6 8 I 5 7 12 J 12 13 14 K 1 3 4 ? a. What are the critical path activities? b. What is the expected time to complete the project? c. What.
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42. MegaSports, Inc. produces two high-priced metal baseball bats, the Slugger and the Launcher, that are made from special aluminum and steel alloys. The cost to produce a Slugger bat is $100, and the cost to produce a Launcher bat is $120. We can not assume that MegaSports will sell.
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1. The LP Relaxation contains the objective function and constraints of the IP problem, but drops all integer restrictions. a. True b. False 2. In general, rounding large values of decision variables to the nearest integer value causes fewer problems than rounding small values. a. True b. False 3. The solution to the LP Relaxation of.
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44. Skooter's Skateboards produces two models of skateboards, the FX and the ZX. Skateboard revenue (in $l,000s) for the firm is nonlinear and is stated as (number of FXs)(5 − 0.2 number of FXs) + (number of ZXs)(7 − 0.3 number of ZXs). Skooter's has 80 labor-hours available per week.
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52. Tom's Tailoring has five idle tailors and four custom garments to make. The estimated time (in hours) it would take each tailor to make each garment is listed below. (An 'X' in the table indicates an unacceptable tailor-garment assignment.) ?? ? Tailor Garment 1 2 3 4 5 Wedding gown 19 23 20 21 18 Clown costume 11 14 X 12 10 Admiral's uniform 12 8 11 X 9 Bullfighter's outfit X 20 20 18 21 ? Formulate and solve an integer program for.
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61. ? A project has the following activities, durations, costs, and precedence relationships: ? ? ? Activity Present Duration (Weeks) Accelerated Duration (Weeks) Immediate Predecessor Activities ? Present Cost ? Accelerated Cost A 10 9 -- $11,000 $15,000 B 15 13 -- 20,000 25,000 C 10 6 A 9,000 20,000 D 20 18 A 25,000 30,000 E 15 10 C 20,000 35,000 F 17 15 B 20,000 30,000 G 12 10 B 15,000 25,000 H 9 8 D,F 12,000 18,000 I 7 6 G,H 10,000 15,000 ? Develop a cost-time trade-off analysis. Detail the steps that you would use to accelerate or crash the project to its minimum duration at the lowest cost. Determine each step's cost and the duration of.
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48. A project network is shown below. Use a forward and a backward pass to determine the critical path, and then fill out the table below. Activity times are in weeks. Activity PrecedenceActivities ActivityTime (weeks) ES LS EF LF Slack CriticalPath? A B C D E F G H I Now assume that the times listed are only the expected times instead of being fixed times. Is the probability.
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11. For a minimization problem, a point is a global minimum if there are no other feasible points with a smaller objective function value. a. True b. False 12. There are nonlinear applications in which there is a single local optimal solution that is also the global optimal solution. a. True b. False 13. Functions that.
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21. ?The normal distribution tends to be a better approximation of the distribution of total time for shorter projects where the critical path has relatively few activities. a. True b. False 22. PERT and CPM a. are most valuable when a small number of activities must be scheduled. b. have different features and are not.
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62. National Oil Company (NATOCO) must plan the shutdown of its Houston refinery for routine preventive maintenance. Each hour of downtime is lost production time and is very costly, so NATOCO wants the maintenance project completed in 22 hours. The PERT network below shows the precedence relationships of the activities.
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31. To determine how to crash activity times a. normal activity costs and costs under maximum crashing must be known. b. shortest times with crashing must be known. c. realize that new paths may become critical. d. All of the alternatives are true. 32. Slack equals a. LF − EF. b. EF − LF. c. EF − LS. d..
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51. Given the following all-integer linear program: Max 3x1 + 2x2 s.t. 3x1 + x2 ≤ 9 x1 + 3x2 ≤ 7 −x1 + x2 ≤ 1 x1, x2 ≥ 0 and integer ? a. ? Solve the problem as a linear program ignoring the integer constraints. Show that the optimal solution to the linear program gives fractional values for both.
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11. The product design and market share optimization problem presented in the textbook is formulated as a 0-1 integer linear programming model. a. True b. False 12. The objective of the product design and market share optimization problem presented in the textbook is to choose the levels of each product attribute that will.
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11. In the periodic review model, the order quantity at each review period must be sufficient to cover demand for the review period plus the demand for the following lead time. a. True b. False 12. Periodic review systems require smaller safety stock levels than corresponding continuous review systems. a. True b. False 13. The cost.
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21. The Markowitz mean-variance portfolio model presented in the text is a convex optimization problem. a. True b. False 22. Because most nonlinear optimization codes will terminate with a local optimum, the solution returned by the codes will be the best solution. a. True b. False 23. It is possible for the optimal solution to a.
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31. For the inventory model with planned shortages, the optimal order quantity results in a. annual holding cost = annual ordering cost. b. annual holding cost = annual backordering cost. c. annual ordering cost = annual holding cost + annual backordering cost. d. annual ordering cost = annual holding cost − annual backordering cost. 32..
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45. The Westfall Company has a contract to produce 10,000 garden hoses for a large discount chain. Westfall has four different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same. Machine Fixed Cost to SetUp Production.
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59. ? A project has the following activities, precedence relationships, and time estimates in weeks: ? ? Activity Immediate Predecessor Activities Optimistic Time (to) Most Likely Time (tm) Pessimistic Time (tp) A -- 15 20 25 B -- 8 10 12 C A 25 30 40 D B 15 15 15 E B 22 25 27 F E 15 20 22 G D 20 20 22 ? a. Compute the expected time and variance for each activity. b. Determine the critical path and the expected duration of the project. c. What is the probability that the project will take longer.
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54. Consider the following PERT/CPM network with estimated times in weeks. The project is scheduled to begin on May 1.The three-time estimate approach was used to calculate the expected times and the following table gives the variance for each activity: Activity Variance Activity Variance A 1.1 E 0.3 B 0.5 F 0.6 C 1.2 G 0.6 D 0.8 H 1.0 ? a. Give the expected project completion date and the critical path. b. By what.
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57. The network below shows the flows possible between pairs of six locations. Formulate an LP to find the maximal flow possible from Node 1 to Node 6. ? 58. A network of railway lines connects the main lines entering and leaving a city. Speed limits, track reconstruction, and train length restrictions.
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56. A business manager for a grain distributor is asked to decide how many containers of each of two grains to purchase to fill its 1,600 pound capacity warehouse. The table below summarizes the container size, availability, and expected profit per container upon distribution. ? ? Grain Container Size Containers Available Container Profit A 500 lbs. 3 $1,200 B 600 lbs. 2 $1,500 ? a. Formulate as a linear.
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62. A plant manager for a sporting goods manufacturer is in charge of assigning the manufacture of four new aluminum products to four different departments. Because of varying expertise and workloads, the different departments can produce the new products at various rates. If only one product is to be produced.
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42. Solve the following problem graphically. Min 6X + 11Y s.t. 9X + 3Y ≥ 27 7X + 6Y ≥ 42 4X + 8Y ≥ 32 X, Y ≥ 0 and integer ? a. Graph the constraints for this problem. Indicate all feasible solutions. b. Find the optimal solution to the LP Relaxation. Round up to find a feasible integer solution. Is.
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1. Critical activities are those that can be delayed without delaying the entire project. a. True b. False 2. PERT and CPM are applicable only when there is no dependence among activities. a. True b. False 3. A path through a project network must reach every node. a. True b. False 4. A critical activity can be part of.
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54. Kloos Industries has projected the availability of capital over each of the next three years to be $850,000, $1,000,000, and $1,200,000, respectively. It is considering four options for the disposition of the capital: (1) Research and development of a promising new product (2) Plant expansion (3) Modernization of its current facilities (4) Investment in a valuable piece.
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45. A cookie recipe gives the following numbered steps. 1. Preheat oven. 2. Grease cookie sheets. 3. Cream shortening and sugar. 4. Add eggs and flavoring. 5. Measure and sift dry ingredients. 6. Add dry ingredients to mixture. 7. Drop by spoonfuls onto sheets and bake for 10 minutes. Although the steps are numbered, they do not always reflect immediate precedence relationships. Develop a table.
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49. Consider the problem faced by a summer camp recreation director who is trying to choose activities for a rainy day. Information about possible choices is given in the table below. Category Activity Time(minutes) Popularitywith Campers Popularity withCounselors Art 1 - Painting 30 4 2 2 - Drawing 20 5 2 3 - Nature craft 30 3 1 Music 4 - Rhythm band 20 5 5 Sports 5 - Relay races 45 2 1 6 - Basketball 60 1 3 Computer 7 -.
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64. A computer manufacturing company wants to develop a monthly plan for shipping finished products from three of its manufacturing facilities to three regional warehouses. It is thinking about using a transportation LP formulation to exactly match capacities and requirements. Data on transportation costs (in dollars per unit), capacities, and.
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1. A nonlinear optimization problem is any optimization problem in which at least one term in the objective function or a constraint is nonlinear. a. True b. False 2. A function is quadratic if its nonlinear terms have a power of 4. a. True b. False 3. Nonlinear programming algorithms are more complex than linear programming.
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31. A convex function is a. bowl-shaped up. b. bowl-shaped down. c. elliptical in shape. d. sinusoidal in shape. 32. If the coefficient of each squared term in a quadratic function is positive, the function is a. concave. b. convex. c. elliptical. d. sinusoidal. 33. Components that share a storage facility are called a. constrained components. b. indexed components. c. blended components. d. pooled.
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