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operations research an introduction

Questions and Answers of Operations Research An Introduction

Suppose on April 8, 2001, we paid out $900. Then we receive $300 on 8/15/01 $400 on 1/15/02 $200 on 6/25/02 $100 on 7/03/03.If the annual discount rate is 10%, what is the NPV of these cash flows?
Star Oil Company is considering five different investment opportunities. The cash outflows and net present values (in millions of dollars) are given in Table 7. Star Oil has $40 million available for
1 Show that if r 0.02, investment 2 has a larger NPV than investment 1.
2 Two investments with varying cash flows (in thousands of dollars) are available, as shown in Table 8. At time 0, $10,000 is available for investment, and at time 1, $7,000 is available. Assuming
3 Suppose that r, the annual interest rate, is 0.20, and that all money in the bank earns 20% interest each year (that is, after being in the bank for one year, $1 will increase to$1.20). If we place
4 A company has nine projects under consideration. The NPV added by each project and the capital required by each project during the next two years is given in Table 9. All figures are in millions.
5 Finco must determine how much investment and debt to undertake during the next year. Each dollar invested reduces the NPV of the company by 10¢, and each dollar of debt increases the NPV by 50¢
Semicond is a small electronics company that manufactures tape recorders and radios. The per-unit labor costs, raw material costs, and selling price of each product are given in Table 10. On December
1 Graphically solve the Semicond problem.
2 Suppose that the January 1 inventory shipment had been valued at $7,000. Show that Semicond’s LP is now infeasible
Sunco Oil manufactures three types of gasoline (gas 1, gas 2, and gas 3). Each type is produced by blending three types of crude oil (crude 1, crude 2, and crude 3). The sales price per barrel of
1 You have decided to enter the candy business. You are considering producing two types of candies: Slugger Candy and Easy Out Candy, both of which consist solely of sugar, nuts, and chocolate. At
2 O.J. Juice Company sells bags of oranges and cartons of orange juice. O.J. grades oranges on a scale of 1 (poor)to 10 (excellent). O.J. now has on hand 100,000 lb of grade 9 oranges and 120,000 lb
3 A bank is attempting to determine where its assets should be invested during the current year. At present,$500,000 is available for investment in bonds, home loans, auto loans, and personal loans.
4 Young MBA Erica Cudahy may invest up to $1,000. She can invest her money in stocks and loans. Each dollar invested in stocks yields 10¢ profit, and each dollar invested in a loan yields 15¢
5 Chandler Oil Company has 5,000 barrels of oil 1 and 10,000 barrels of oil 2. The company sells two products:gasoline and heating oil. Both products are produced by combining oil 1 and oil 2. The
6 Bullco blends silicon and nitrogen to produce two types of fertilizers. Fertilizer 1 must be at least 40% nitrogen and sells for $70/lb. Fertilizer 2 must be at least 70% silicon and sells for
7 Eli Daisy uses chemicals 1 and 2 to produce two drugs.Drug 1 must be at least 70% chemical 1, and drug 2 must be at least 60% chemical 2. Up to 40 oz of drug 1 can be sold at $6 per oz; up to 30 oz
8 Highland’s TV-Radio Store must determine how many TVs and radios to keep in stock. A TV requires 10 sq ft of floorspace, whereas a radio requires 4 sq ft; 200 sq ft of floorspace is available. A
9 Linear programming models are used by many Wall Street firms to select a desirable bond portfolio. The following is a simplified version of such a model. Solodrex is considering investing in four
10 Coalco produces coal at three mines and ships it to four customers. The cost per ton of producing coal, the ash and sulfur content (per ton) of the coal, and the production capacity (in tons) for
11 Eli Daisy produces the drug Rozac from four chemicals. Today they must produce 1,000 lb of the drug.The three active ingredients in Rozac are A, B, and C. By weight, at least 8% of Rozac must
12 (A spreadsheet might be helpful on this problem.) The risk index of an investment can be obtained from return on investment (ROI) by taking the percentage of change in the value of the investment
13 The owner of Sunco does not believe that our LP optimal solution will maximize daily profit. He reasons,“We have 14,000 barrels of daily refinery capacity, but your optimal solution produces
14 Oilco produces two products: regular and premium gasoline. Each product contains .15 gram of lead per liter.The two products are produced from six inputs: reformate, fluid catalytic cracker
Rylon Corporation manufactures Brute and Chanelle perfumes. The raw material needed to manufacture each type of perfume can be purchased for $3 per pound. Processing 1 lb of raw material requires 1
Sunco Oil has three different processes that can be used to manufacture various types of gasoline. Each process involves blending oils in the company’s catalytic cracker.Running process 1 for an
2 Furnco manufactures tables and chairs. A table requires 40 board ft of wood, and a chair requires 30 board ft of wood. Wood may be purchased at a cost of $1 per board ft, and 40,000 board ft of
3 Suppose that in Example 11, 1 lb of raw material could be used to produce either 3 oz of Brute or 4 oz of Chanelle.How would this change the formulation?
4 Chemco produces three products: 1, 2, and 3. Each pound of raw material costs $25. It undergoes processing and yields 3 oz of product 1 and 1 oz of product 2. It costs$1 and takes 2 hours of labor
5 A company produces A, B, and C and can sell these products in unlimited quantities at the following unit prices:A, $10; B, $56; C, $100. Producing a unit of A requires 1 hour of labor; a unit of B,
6 Daisy Drugs manufactures two drugs: 1 and 2. The drugs are produced by blending two chemicals: 1 and 2. By weight, drug 1 must contain at least 65% chemical 1, and drug 2 must contain at least 55%
7 Lizzie’s Dairy produces cream cheese and cottage cheese. Milk and cream are blended to produce these two products. Both high-fat and low-fat milk can be used to produce cream cheese and cottage
8 A company produces six products in the following fashion. Each unit of raw material purchased yields four units of product 1, two units of product 2, and one unit of product 3. Up to 1,200 units of
9 Each week Chemco can purchase unlimited quantities of raw material at $6/lb. Each pound of purchased raw material can be used to produce either input 1 or input 2.Each pound of raw material can
10 LIMECO owns a lime factory and sells six grades of lime (grades 1 through 6). The sales price per pound is given in Table 25. Lime is produced by kilns. If a kiln is run for an 8-hour shift, the
11 Chemco produces three products: A, B, and C. They can sell up to 30 pounds of each product at the following prices (per pound): product A, $10; product B, $12; product C, $20. Chemco purchases raw
12 Chemco produces 3 chemicals: B, C, and D. They begin by purchasing chemical A for a cost of $6/100 liters. For anadditional cost of $3 and the use of 3 hours of skilled labor, 100 liters of A can
13 Carrington Oil produces two types of gasoline, gas 1 and gas 2, from two types of crude oil, crude 1 and crude 2. Gas 1 is allowed to contain up to 4% impurities, and gas 2 is allowed to contain
14 You have been put in charge of the Melrose oil refinery.The refinery produces gas and heating oil from crude oil.Gas sells for $8 per barrel and must have an average “grade level” of at least
Sailco Corporation must determine how many sailboats should be produced during each of the next four quarters (one quarter three months). The demand during each of the next four quarters is as
1 A customer requires during the next four months, respectively, 50, 65, 100, and 70 units of a commodity (no backlogging is allowed). Production costs are $5, $8, $4, and $7 per unit during these
2 A company faces the following demands during the next three periods: period 1, 20 units; period 2, 10 units; period 3, 15 units. The unit production cost during each period is as follows: period
3 James Beerd bakes cheesecakes and Black Forest cakes.During any month, he can bake at most 65 cakes. The costs per cake and the demands for cakes, which must be met on time, are listed in Table 33.
4 A manufacturing company produces two types of products: A and B. The company has agreed to deliver the products on the schedule shown in Table 34. The company has two assembly lines, 1 and 2, with
5 During the next two months, General Cars must meet(on time) the following demands for trucks and cars: month 1—400 trucks, 800 cars; month 2—300 trucks, 300 cars.During each month, at most
6 Gandhi Clothing Company produces shirts and pants.Each shirt requires 2 sq yd of cloth, each pair of pants, 3.During the next two months, the following demands for shirts and pants must be met (on
7 Each year, Paynothing Shoes faces demands (which must be met on time) for pairs of shoes as shown in Table 37. Workers work three consecutive quarters and then receive one quarter off. For example,
8 A company must meet (on time) the following demands:quarter 1—30 units; quarter 2—20 units; quarter 3—40 units. Each quarter, up to 27 units can be produced with regular-time labor, at a cost
9 Donovan Enterprises produces electric mixers. During the next four quarters, the following demands for mixers must be met on time: quarter 1—4,000; quarter 2—2,000;quarter 3—3,000; quarter
Finco Investment Corporation must determine investment strategy for the firm during the next three years. Currently (time 0), $100,000 is available for investment. Investments A, B, C, D, and E are
1 A consultant to Finco claims that Finco’s cash on hand at time 3 is the sum of the cash inflows from all investments, not just those investments yielding a cash inflow at time 3.Thus, the
2 Show that Finco’s objective function may also be written as max z=> 100,000 +0.54 + 0.5B+ 0.2C+0.9D + 0.5E + 0.08S+ 0.08S + 0.0852
3 At time 0, we have $10,000. Investments A and B are available; their cash flows are shown in Table 39. Assume that any money not invested in A or B earns no interest.Formulate an LP that will
4 Broker Steve Johnson is currently trying to maximize his profit in the bond market. Four bonds are available for purchase and sale, with the bid and ask price of each bond as shown in Table 40.
5 A small toy store, Toyco projects the monthly cash flows(in thousands of dollars) in Table 42 during the year 2003.A negative cash flow means that cash outflows exceed cash inflows to the business.
6 Consider Problem 5 with the following modification:Each month Toyco can delay payments on some or all of the cash owed for the current month. This is called “stretching payments.” Payments may
7 Suppose we are borrowing $1,000 at 12% annual interest with 60 monthly payments. Assume equal payments are made at the end of month 1, month 2, . . . month 60. We know that entering into Excel the
8 You are a CFA (chartered financial analyst). Madonna has come to you because she needs help paying off her credit card bills. She owes the amounts on her credit cards shown in Table 43. Madonna is
9 Winstonco is considering investing in three projects. If we fully invest in a project, the realized cash flows (in millions of dollars) will be as shown in Table 44. For example, project 1 requires
CSL is a chain of computer service stores. The number of hours of skilled repair time that CSL requires during the next five months is as follows:Month 1 (January): 6,000 hours Month 2 (February):
1 If y1= 38, then what would be the optimal solution to CSL’s problem?
2 An insurance company believes that it will require the following numbers of personal computers during the next six months: January, 9; February, 5; March, 7; April, 9;May, 10; June, 5. Computers
3 The IRS has determined that during each of the next 12 months it will need the number of supercomputers given in Table 45. To meet these requirements, the IRS rentsvsupercomputers for a period of
4 You own a wheat warehouse with a capacity of 20,000 bushels. At the beginning of month 1, you have 6,000 bushelsof wheat. Each month, wheat can be bought and sold at the price per 1000 bushels
1 Bloomington Breweries produces beer and ale. Beer sells for $5 per barrel, and ale sells for $2 per barrel.Producing a barrel of beer requires 5 lb of corn and 2 lb of hops. Producing a barrel of
2 Farmer Jones bakes two types of cake (chocolate and vanilla) to supplement his income. Each chocolate cake can be sold for $1, and each vanilla cake can be sold for 50¢.Each chocolate cake
3 I now have $100. The following investments are available during the next three years:Investment A Every dollar invested now yields $0.10 a year from now and $1.30 three years from now.Investment B
4 Sunco processes oil into aviation fuel and heating oil. It costs $40 to purchase each 1,000 barrels of oil, which is then distilled and yields 500 barrels of aviation fuel and 500 barrels of
5 Finco has the following investments available:Investment A For each dollar invested at time 0, we receive$0.10 at time 1 and $1.30 at time 2. (Time 0 now;time 1 one year from now; and so
6 All steel manufactured by Steelco must meet the following requirements: 3.2–3.5% carbon; 1.8–2.5% silicon;0.9–1.2% nickel; tensile strength of at least 45,000 pounds per square inch (psi).
7 Steelco manufactures two types of steel at three different steel mills. During a given month, each steel mill has 200 hours of blast furnace time available. Because of differences in the furnaces
8 Walnut Orchard has two farms that grow wheat and corn. Because of differing soil conditions, there are differences in the yields and costs of growing crops on the two farms. The yields and costs
9 Candy Kane Cosmetics (CKC) produces Leslie Perfume, which requires chemicals and labor. Two production processes are available: Process 1 transforms 1 unit of labor and 2 units of chemicals into 3
10 Carco has a $150,000 advertising budget. To increase automobile sales, the firm is considering advertising in newspapers and on television. The more Carco uses a particular medium, the less
11 Sunco Oil has refineries in Los Angeles and Chicago.The Los Angeles refinery can refine up to 2 million barrels of oil per year, and the Chicago refinery up to 3 million.Once refined, oil is
12 For a telephone survey, a marketing research group needs to contact at least 150 wives, 120 husbands, 100 single adult males, and 110 single adult females. It costs $2 to make a daytime call and
13 Feedco produces two types of cattle feed, both consisting totally of wheat and alfalfa. Feed 1 must contain at least 80% wheat, and feed 2 must contain at least 60%alfalfa. Feed 1 sells for
Feedco (see Problem 13) has decided to give its customer (assume it has only one customer) a quantity discount. If the customer purchases more than 300 lb of feed 1, each pound over the first 300 lb
15 Chemco produces two chemicals: A and B. These chemicals are produced via two manufacturing processes.Process 1 requires 2 hours of labor and 1 lb of raw material to produce 2 oz of A and 1 oz of
16 Suppose that in the CSL computer example of Section 3.12, it takes two months to train a technician and that during the second month of training, each trainee requires 10 hours of experienced
17 Furnco manufactures tables and chairs. Each table and chair must be made entirely out of oak or entirely out of pine. A total of 150 board ft of oak and 210 board ft of pine are available. A table
18 The city of Busville contains three school districts.The number of minority and nonminority students in each district is given in Table 53. Of all students, 25% (200/800) are minority students.The
19 Brady Corporation produces cabinets. Each week, it requires 90,000 cu ft of processed lumber. The company may obtain lumber in two ways. First, it may purchase lumber from an outside supplier and
20 The Canadian Parks Commission controls two tracts of land. Tract 1 consists of 300 acres and tract 2, 100 acres.Each acre of tract 1 can be used for spruce trees or hunting, or both. Each acre of
21 Chandler Enterprises produces two competing products: A and B. The company wants to sell these products to two groups of customers: group 1 and group 2. The value each customer places on a unit of
22 Alden Enterprises produces two products. Each product can be produced on one of two machines. The length of time needed to produce each product (in hours) on each machine is as shown in Table 57.
23 Kiriakis Electronics produces three products. Each product must be processed on each of three types of machines. When a machine is in use, it must be operated by a worker. The time (in hours)
24 Gotham City Hospital serves cases from four diagnostic-related groups (DRGs). The profit contribution, diagnostic service use (in hours), bed-day use (in days), nursing care use (in hours), and
25 Oliver Winery produces four award-winning wines in Bloomington, Indiana. The profit contribution, labor hours, and tank usage (in hours) per gallon for each type of wine are given in Table 61. By
26 Graphically solve the following LP: min z = 5x1 + s.t. 2x1 + x2 x26 x + 4 2x + 10x220 x1,x20
27 Grummins Engine produces diesel trucks. New government emission standards have dictated that the average pollution emissions of all trucks produced in the next three years cannot exceed 10 grams
28 Describe all optimal solutions to the following LP: min z = 4x1 + x2 s.t. 3x1 + x2 6 4x1 + x2 12 x1 2 x1,x20
29 Juiceco manufactures two products: premium orange juice and regular orange juice. Both products are made by combining two types of oranges: grade 6 and grade 3. The oranges in premium juice must
30 Graphically solve the following linear programming problem: max z = 5x - x2 s.t. 2x + 3x2 12 x1-3x20 x0,x20
31 Graphically find all solutions to the following LP: min zx12x2 = x1 s.t. x + x1 4 x2 = 8 28 x2 6 x26 x1, x20
32 Each day Eastinghouse produces capacitors during three shifts: 8 A.M.–4 P.M., 4 P.M.–midnight, midnight–8 A.M.The hourly salary paid to the employees on each shift, the price charged for
33 Graphically find all solutions to the following LP: max z = 4x1 + x2 s.t. 8x1 + 2x2 16 x1 + x2 12 X1, X2 20
34 During the next three months Airco must meet (on time) the following demands for air conditioners: month 1, 300; month 2, 400; month 3, 500. Air conditioners can be produced in either New York or
35 Formulate the following as a linear programming problem: A greenhouse operator plans to bid for the job of providing flowers for city parks. He will use tulips, daffodils, and flowering shrubs in

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