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operations research an introduction

Questions and Answers of Operations Research An Introduction

10 Explain how by solving a single transshipment problem you can find the shortest path from node 1 in a network to each other node in the network. TABLE 7 Box 1 2 3 4 5 6 7 Size 33 30 26 Demand 400
3 Given the continuous triangular distribution in Figure 13, develop a process generator using the inverse transformation method. FIGURE 13 fx) 0.2 2 8 12
3 I must drive from Bloomington to Cleveland. Several paths are available (see Figure 4). The number on each arc is the length of time it takes to drive between the two cities.For example, it takes 3
8 A library must build shelving to shelve 200 4-inch high books, 100 8-inch high books, and 80 12-inch high booksEach book is 0.5 inch thick. The library has several ways to store the books. For
2 A job shop manager wants to develop a simulation model to help schedule jobs through the shop. He has evaluated the completion times for all the different types of jobs. For one particular job, the
2 A sales representative lives in Bloomington and must bein Indianapolis next Thursday. On each of the days Monday, Tuesday, and Wednesday, he can sell his wares in Indianapolis, Bloomington, or
1 Consider a continuous random variable with the following pdf:Develop a process generator for these breakdown times using the inverse transformation method and the acceptance–rejection method.
1 Find the shortest path from node 1 to node 10 in the network shown in Figure 3. Also, find the shortest path from node 3 to node 10. FIGURE 3 7 1 /m 3 4 160 + 5 a 3 2 3 10 5 7 3
5 Suppose it costs $10,000 to purchase a new car. The annual operating cost and resale value of a used car are shown in Table 4. Assuming that one now has a new car, determine a replacement policy
Use the acceptance–rejection method to generate random variates from a triangular distribution whose pdf is given by f(x) = *2 9 12- 21 + 2/1 - 1 = 85x59 2 x 6
Consider a random variable X whose pdf is given byUse the ITM to generate observations from the distribution. This distribution, called a triangular distribution, is represented graphically in Figure
4 Use Dijkstra’s algorithm to find the shortest path from node 1 to node 4 in Figure 5. Why does Dijkstra’s algorithm fail to obtain the correct answer? Network for Problem 2 1 00 8 2 5. 2 4 12 5
Consider a random variable X that is uniformly distributed on the interval [a, b]. The pdf of this distribution is given by the functionUse the ITM to generate observations from this random variable.
As mentioned in Chapter 20, the exponential distribution has important applications in the mathematical representation of queuing systems. The pdf of the exponential distribution is given byUse the
I have a 9-oz cup and a 4-oz cup. My mother has ordered me to bring home exactly 6 oz of milk. How can I accomplish this goal? TABLE 1 Moves in the Cup-and-Milk Problem No. of Ounces in 9-oz Cup No.
Let us consider the Powerco example (Figure 2). Suppose that when power is sent from plant 1 (node 1) to city 1 (node 6), it must pass through relay substations (nodes 2–5).For any pair of nodes
1 A consulting firm is trying to determine how to minimize the annual costs associated with purchasing computer paper.Each time an order is placed an ordering cost of $20 is incurred. The price per
6 Consider a knapsack problem for whichShow that if the knapsack can hold w pounds, and w >= w*, wherethen the optimal solution to the knapsack problem must use at least one Type 1 item. L WI > C2
8 A large car dealership in Bloomington, Indiana, employsfive salespeople. All salespeople work on commission; they are paid a percentage of the profits from the cars they sell.The dealership has
2 Each year, Shopalot Stores sells 10,000 cases of soda.The company is trying to determine how many cases should be ordered each time. It costs $5 to process each order, and the cost of carrying a
An auto repair shop always needs to have an engine analyzer available. A new engine an lyzer costs $1,000. The cost mi of maintaining an engine analyzer during its ith year of operation is as
9 Consider a bank with 4 tellers. Customers arrive at anexponential rate of 60 per hour. A customer goes directly into service if a teller is idle. Otherwise, the arrival joins a waiting line. There
find the maximum flow from source to sink. Also find a cut whose capacity equals the maximum flow in the network. 50 6 2 6 3 si 2 1 4 4
3 A firm buys a product using the price schedule given in Table 5. The company estimates holding costs at 10% of purchase price per year and ordering costs at $40 per order.The firm’s annual demand
10 Jobs arrive at a workshop, which has two work centers(A and B) in series, at an exponential rate of 5 per hour.Each job requires processing at both these work centers, first on A and then on B.
find the maximum flow from source to sink. Also find a cut whose capacity equals the maximum flow in the network. 6 6 3 9 7 8 50 2 6 7 6 4 6 si
4 A hospital orders its thermometers from a hospital supply firm. The cost per thermometer depends on the order size q, as shown in Table 6. The annual holding cost is 25%of the purchasing cost. Let
2 Suppose that a new car costs $10,000 and that the annual operating cost and resale value of the car are as shown in Table 13. If I have a new car now, determine a replacement policy that minimizes
3 It costs $40 to buy a telephone from a department store.The estimated maintenance cost for each year of operation is shown in Table 14. (I can keep a telephone for at most five years.) I have just
15 Fly-by-Night Airlines is considering flying three flights.The revenue from each flight and the airports used by each flight are shown in Table 11. When Fly-by-Night uses an airport, the company
Widgetco is about to introduce a new product (product 3). One unit of product 3 is produced by assembling 1 unit of product 1 and 1 unit of product 2. Before production begins on either product 1 or
1 What problem would arise if the network in Figure 39 were a portion of a project network? FIGURE 39 Network for Problem 1 1 2 3
5 Consider the (simplified) list of activities and predecessors that are involved in building a house (Table 20).a Draw a project network, determine the critical path, find the total float for each
Ohm City Appliances has three types of TVs delivered from Springfield TV. Figure 14 gives the annual demand, unit purchasing cost, annual holding cost (as a percentage of purchase cost), the fixed
5 To graduate from State University, Angie Warner needs to pass at least one of the three subjects she is taking this semester. She is now enrolled in French, German, and statistics. Angie’s busy
1 Square City Appliance orders four types of washing machines. Table 7 gives the annual demand, purchasing cost, and annual holding cost (as a percentage of purchase cost), and the fixed cost of
8 The LINDO output in Figure 41 can be used to determine the critical path for Problem 5. Use this output to do the following:a Draw the project diagram.b Determine the length of the critical path
3 A camera store sells an average of 100 cameras per month.The cost of holding a camera in inventory for a year is 30%of the price the camera shop pays for the camera. It costs$120 each time the
13 The government is going to build a high-speed computer in Austin, Texas. Once the computer is designed(D), we can select the exact site (S), the building contractor(C), and the operating personnel
4 A company inventories two items. The relevant data for each item are shown in Table 9. Determine the optimal inventory policy if no shortages are allowed and if the average investment in inventory
Find the critical path, total float, and free float for each activity in the project networks FIGURE 44 B3 F4 G5 6 15. A3 C4 J4 I 2 5 E3 D3 4 K2 H6 L6 8
4 Each year, Data Corporal produces as many as 400 computers in Boston and 300 computers in Raleigh. Los Angeles customers must receive 400 computers, and 300 computers must be supplied to Austin
12 A job shop has four jobs that must be processed on a single machine. The due date and processing time for each job are given in Table 19. Use dynamic programming to determine the order in which
Find the critical path, total float, and free float for each activity in the project networks FIGURE 43 A2 2 B6 3 C4 4 E2 Fl D4 G2 6 HI
15 Consider the project diagram in Figure 42. This project must be completed in 90 days. The time required to complete each activity can be reduced by up to five days at the costs given in Table
6 Workco must have the following number of workers available during the next three months: month 1, 20; month 2, 16; month 3, 25. At the beginning of month 1, Workco has no workers. It costs Workco
8 Daisymay Van Line moves people between New York, Philadelphia, and Washington, D.C. It takes a van one day to travel between any two of these cities. The company incurs costs of $1,000 per day for
4 Indianapolis Airlines has been told that it may schedule six flights per day departing from Indianapolis. The destination of each flight may be New York, Los Angeles,or Miami. Table 20 shows the
6 A company needs to have a working machine during each of the next six years. Currently, it has a new machine.At the beginning of each year, the company may keep the machine or sell it and buy a new
3 In this problem, we explain why the MST algorithm works. Define S = minimum spanning tree Ct = nodes connected after iteration t of MST algorithm has been completed Ct= nodes not connected after
9 For a computer to work properly, three subsystems of the computer must all function properly. To increase the reliability of the computer, spare units may be added to each system. It costs $100 to
10 During any year, I can consume any amount that does not exceed my current wealth. If I consume c dollars during a year, I earn ca units of happiness. By the beginning of the next year, the
2 For the MCNFP in Figure 62, find a bfs. FIGURE 62 00 $11 2 25 $10 00 $7 $8 (40) 1 25 $12 3 25 $7 00 $5 6 (-40) $5 25 $6 10 5 00 $3
3 Find the optimal solution to the MCNFP in Figure 63 using the bfs in Figure 64 as a starting basis FIGURE 63 30 $5 2 4(-22) (32) 1 25 $15 00 $5 20 $10 * $14 12 $4 12 $11 3 5 (-10) 00 $5 FIGURE 64
4 Find a bfs for the network in Figure 65. FIGURE 65 3 (10) (10) (1 15 (10) 2 13 24 12 6 9 7 4 6 (-20) 24 15 5
5 Find the optimal solution to the MCNFP in Figure 66 using the bfs in Figure 67 as a starting basis. FIGURE 66 30 $10 75 $15 50 $10 60 $30 100 $45 40 $10 (-25) (100) 40 $5 5 100 $45 50 $10 40 $25 40
1 A truck must travel from New York to Los Angeles. As shown in Figure 68, a variety of routes are available. The number associated with each arc is the number of gallons of fuel required by the
2 Telephone calls from New York to Los Angeles are transported as follows: The call is sent first to either Chicago or Memphis, then routed through either Denver or Dallas, and finally sent to Los
3 Before a new product can be introduced, the activities in Table 40 must be completed (all times are in weeks).a Draw the project diagram.b Determine all critical paths and critical activities.c
6 A company produces a product at two plants, 1 and 2.The unit production cost and production capacity during each period are given in Table 41. The product is instantaneously shipped to the
7 A project is considered completed when activities A–F have all been completed. The duration and predecessors of each activity are given in Table 43. The LINDO output in Figure 69 can be used to
8 State University has three professors who each teachfour courses per year. Each year, four sections of marketing, finance, and production must be offered. At least one section of each class must be
9 During the next two months, Machineco must meet (on time) the demands for three types of products shown in Table 45. Two machines are available to produce theseproducts. Machine 1 can only produce
What Is LINGO?
28 Suppose the bfs for an optimal tableau is degenerate, and a nonbasic variable in row 0 has a zero coefficient.Show by example that either of the following cases may hold:Case 1 The LP has more
27 Suppose we have found an optimal tableau for an LP, and the bfs for that tableau is nondegenerate. Also suppose that there is a nonbasic variable in row 0 with a zero coefficient. Prove that the
26 Carco uses robots to manufacture cars. The following demands for cars must be met (not necessarily on time, but all demands must be met by end of quarter 4): quarter 1—600; quarter 2—800;
25 Ghostbusters, Inc., exorcises (gets rid of) ghosts.During each of the next three months, the company will receive the following number of calls from people who want their ghosts exorcised:
24 During the next four quarters, Dorian Auto must meet(on time) the following demands for cars: quarter 1—4,000;quarter 2—2,000; quarter 3—5,000; quarter 4—1,000. At the beginning of quarter
22 Monroe County is trying to determine where to place the county fire station. The locations of the county’s four major towns are given in Figure 31. Town 1 is at (10, 20);town 2 is at (60, 20);
21 Shoemakers of America forecasts the following demand for each of the next six months: month 1—5,000 pairs;month 2—6,000 pairs; month 3—5,000 pairs; month 4—9,000 pairs; month 5—6,000
20 A bus company believes that it will need the following number of bus drivers during each of the next five years:year 1—60 drivers; year 2—70 drivers; year 3—50 drivers;year 4—65 drivers;
19 Suppose we are solving a maximization problem and the variable xr is about to leave the basis.a What is the coefficient of xr in the current row 0?b Show that after the current pivot is performed,
17 You are given the tableau shown in Table 74 for a maximization problem. Give conditions on the unknowns a1, a2, a3,b, and c that make the following statements true:a The current solution is
15 Consider a maximization problem with the optimal tableau in Table 73. The optimal solution to this LP is z 10, x3 3, x4 5, x1 x2 0. Determine the second-best bfs to this LP. (Hint: Show
12 Productco produces three products. Each product requires labor, lumber, and paint. The resource requirements, unit price, and variable cost (exclusive of raw materials) for each product are given
10 Suppose that in the Dakota Furniture problem, 10 types of furniture could be manufactured. To obtain an optimal solution, how many types of furniture (at the most) would have to be manufactured?
Use Excel Solver to find the optimal solution to the following problems:Problem 5 of Section 3.12
Use Excel Solver to find the optimal solution to the following problems:Problem 3 of Section 3.12
Use Excel Solver to find the optimal solution to the following problems:Problem 5 of Section 3.11
Use Excel Solver to find the optimal solution to the following problems:Problem 4 of Section 3.11
Use Excel Solver to find the optimal solution to the following problems:Example 14 of Section 3.12
Use Excel Solver to find the optimal solution to the following problems:4 Problem 3 of Section 3.10
Use Excel Solver to find the optimal solution to the following problems:3 Example 11 of Chapter 3
Use Excel Solver to find the optimal solution to the following problems:2 Example 7 of Chapter 3
Use Excel Solver to find the optimal solution to the following problems: 1 Problem 2 of Section 3.4
13 The new president has just been elected and has set the following economic goals (listed from highest to lowest priority):Goal 1 Balance the budget (this means revenues are at least as large as
8 Faber College is admitting students for the class of 2008. It has set four goals for this class, listed in order of priority:Goal 1 Entering class should be at least 5,000 students.Goal 2 Entering
7 There are four teachers in the Faber College Business School. Each semester, 200 students take each of the following courses: marketing, finance, production, and statistics. The “effectiveness”
5 Deancorp produces sausage by blending together beef head, pork chuck, mutton, and water. The cost per pound, fat per pound, and protein per pound for these ingredients is given in Table 59.
3 Highland Appliance must determine how many color TVs and VCRs should be stocked. It costs Highland $300 to purchase a color TV and $200 to purchase a VCR. A color TV requires 3 sq yd of storage
2 Fruit Computer Company is ready to make its annual purchase of computer chips. Fruit can purchase chips (in lots of 100) from three suppliers. Each chip is rated as being of excellent, good, or
1 Graphically determine the preemptive goal progamming solution to the Priceler example for the following priorities:a LIP is highest-priority goal, followed by HIW and then HIM.b HIM is
The Leon Burnit Advertising Agency is trying to determine a TV advertising schedule for Priceler Auto Company. Priceler has three goals:Goal 1 Its ads should be seen by at least 40 million
7 Clothco manufactures pants. During each of the next six months they can sell up to the numbers of pants given in Table 51.Demand that is not met during a month is lost. Thus, for example, Clothco
6 Show that after any number of pivots the coefficient of xi in each row of the simplex tableau will equal the negative of the coefficient of xi in the same row.
5 Steelco’s main plant currently has a steel manufacturing area and shipping area located as shown in Figure 13(distances are in feet). The company must determine where to locate a casting facility
3 During the next three months, Steelco faces the following demands for steel: 100 tons (month 1); 200 tons(month 2); 50 tons (month 3). During any month, a worker can produce up to 15 tons of steel.
1 Suppose that Mondo no longer must meet demands on time. For each quarter that demand for a motorcycle is unmet, a penalty or shortage cost of $110 per motorcycle short is assessed. Thus, demand can
Mondo Motorcycles is determining its production schedule for the next four quarters. Demand for motorcycles will be as follows: quarter 1—40; quarter 2—70; quarter 3—50;quarter 4—20. Mondo

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