Question;Module 1;Chapter;Problems;1;2, 4;2;10, 12, 14;Chapter 1;Question2;The Retread Tire Company recaps tires. The fixed annual costof the recapping;operation is $ 60,000. The variable cost ifrecapping tires is $9. The company;charges $25 to recap atire.a) For an annual volume of 120,000 tires, determine;the totalcost, total revenue, and profit.b) Determine the annual break-even;volume for the Retread TireCompany operation.;Problem 4;Evergreen Fertilizer Company produces fertilizer. thecompany's fixed monthly;cost is $25, 000 and its variable cost perpound of fertilizer is $0.15.;Evergreen sells the fertilizer for$0.40 per pound. Determine the monthly;break-even volume for thecompany.;Chapter 2;Problem 10;A large research hospital has accumulated statistical data on its patients for;an extended period. Researchers have determined that patients who are smokers;have an 18% chance of contracting a serious illness such as heart disease, cancer;of emphysema, whereas there is only a.06 probability that a nonsmoker will;contract a serious illness. From hospital records, the researchers know that;23% of all hospital patients are smokers, while 77% are nonsmokers. For;planning purposes, the hospital physician staff would like to know the;probability that a gives patient is a smoker if the patient has a serious;illness.;Problem 12;the senate consist of 100 senators, of whom 34 are republicans and 66 are;democrats. A bil to increase appropriations is before the senate. thirty-five;percent of the democrats and 70% of the republicans favor the bill. the bill;needs a simple majority to pass. using a probability tree, determine the;probability that the bill will pass.;Problem 14;A metropolitan school system consists of three districts ? north, south, and;central. The north district contains 25% of all students, the south district;contains 40% of all students, and the central district contains 35%. A minimum;competency test was given to all students. 10% of the north district students;failed, 15% of the south district students failed, and 5% of the central;district students failed.;A - develop a probability tree showing all marginal, conditional, and joint;probabilities;B - develop a joint probability table.;C - What is the probability that a student selected at random failed the test;Module 2;Chapter;Problems;3;8, 26;problem 3-8;A local real estate investor in Orlando is considering three alternative;investments: a motel, a restaurant, or a theater. Profits from the motel or;restaurant will be affected by the availability of gasoline and the number of;tourists, profits from the theater will be relatively stable under any;conditions. The following payoff table shown the profit or loss that could;result from each investment.;Gasoline Availability;Investment Shortage Stable Supply Surplus;Motel $-8,000 $15,000 $20,000;Restuarant 2,000 8,000 6,000;Theater 6,000 6,000 5,000;Determine the best investment using the following decision criteria.;a. Maximax;b. Maximin;c. Minimax regret;d. Hurwicz (? =.4);e. Equal likelihood;problem 3-26;The Steak and Chop Butcher Shop purchases steak from a local meatpacking house.;The meat is purchased on Monday at $2.00 per pound, and the shop sells the;steak for $3.00 per pound. Any steak left over at the end of the week is sold;to a local zoo for $.50 per pound. The possible demands for steak and the;probability of each are shown in the following table;Demand (lb.) Probability;20.10;21.20;22.30;23.30;24.10;1.00;The shop must decide how much steak to order in a week. Using Excel, construct;a payoff table for this decision situation and determine the amount of steak;that should be ordered, using expected value.;Module 3;Chapter;Problems;4;2, 38;2. The manger of the Carpet City outlet needs to make an accurate forecast;of the demand of Soft Shag carpet (its biggest seller). If the manger does not;order enough carpet from the carpet mill, customer will their carpet from one;of Carpet City's many competitors. The manager has collected the following;demand data for the past 8 months;Demand for Soft Shag;Month Carpet (1,000 yd.);1 8;2 12;3 7;4 9;5 15;6 11;7 10;8 12;a. Compute a 3- month moving average forecast for months 4 through 9.;b. Compute a weighed 3- month moving average forecast for months 4 through 9.;Assign weights of.55,.33, and.12 to the months in sequence, starting with;the most recent month.;c. Compare the two forecasts by using MAD. Which forecast appears to be more;accurate?;6. The manager of the Petroco Service station wants to forecast the demand;for unleaded gasoline next month so that the proper number of gallons can be;ordered from the distributor. The owner has accumulated the following data on;demand for unleaded gasoline from sales during the past 10 months;Month Gasoline Demand (gal);October 800;November 725;December 630;January 500;February 645;March 690;April 730;May 810;June 1200;July 980;a. Compute and exponentially smoothed forecast, using on ? value of;.30.;b. Compute an adjusted exponentially smoothed forecast (with ? =.30;and ?=.20).;c. Compare the two forecast by using MAPD and indicate which seems to be more;accurate.;Problem 4-38;Apperson and Fitz is a chain of clothing stores that caters to high school;and college students. It publishes a quarterly catalog and operates a Web site;that features provocatively attired males and females. The Web site is very;expensive to maintain, and company executives are not sure whether the number;of hits at the site relate to sales (i.e., people may be looking at the site's;pictures only). The Web master has accumulated the following data for hits per;month and orders placed at the Web site for the past 20 months;Month Hits(1,000s) Orders(1,000s);1 34.2 7.6;2 28.5 6.3;3 36.7 8.9;4 42.3 5.7;5 25.8 5.9;6 52.3 6.3;7 35.2 7.2;8 27.9 4.1;9 31.4 3.7;10 29.4 5.9;11 46.7 10.8;12 43.5 8.7;13 52.6 9.3;14 61.8 6.5;15 37.3 4.8;16 28.9 3.1;17 26.4 6.2;18 39.4 5.9;19 44.7 7.2;20 46.3 5.5;Develop a liner regression model for these data and indicate whether there;appears to be a strong relationship between Web site hits and orders. What;would be the forecast for orders with 50,000 hits per month?;Module 4;Chapter;Problems;5;8, 10, 12, 14;6;2, 4;Chapter 5;problem 8. The ticket booth on the Tech campus is operated by one person, who;is selling tickets for the annual Tech versus State football game on Saturday.;The ticket seller can serve an average of 12 customers per hour, on average, 10;customers arrive to purchase tickets each hour.;Determine;the average time a ticket buyer must wait and the portion of time the ticket;seller is busy.;10. The;Dynaco Manufacturing Company produces a particular product in an assembly line;operation. One of the machines on the line is a drill press that has a single;assembly line feeding into it. A partially completed unit arrives at the press;to be worked on every 7.5 minutes, on average. The machine operator can process;an average of 10 parts per hour. Determine the average number of parts waiting;to be worked on, the percentage of time the operator is working, and the;percentage of time the machine is idle.;12. The;Peachtree Airport in Atlanta serves light aircraft. It has a single runway and;one air traffic controller to land planes. It takes an airplane 12 minutes to;land and clear the runway. Planes arrive at the airport at the rate of four per;hour.;a. Determine;the average number of planes that will stack up, waiting to land.;b. Find the average time a plane must wait in line before it can land.;14.;During registration at State University every semester, students in the college;of business must have their courses approved by the college adviser. It takes;the adviser an average of 2 minutes to approve each schedule, and students;arrive at the adviser's office at the rate of 28 per hour.;a.;Compute L, Lq, W, Wq, and U.;b. The dean of the college has received a number of complaints from students;about the length of time they must wait to have their schedules approved. The;dean feels that waiting 10.00 minutes to get a schedule approved is not;unreasonable. Each assistant the dean assigns to the advisor's office will;reduce the average time required to approve a schedule by 0.25 minute, down to;a minimum time of 1.00 minute to approve a schedule. How many assistants should;the dean assign to the adviser?;Chapter 6;problem 2;Hayes;Electronics assumes with certainty that the ordering cost is $450 per order and;the inventory carrying cost is $170 per unit per year.However, the inventory;model parameters are frequently only estimates that are subject to some degree;of uncertainty.Consider four cases of variation in the model parameters as;follows:(a) both ordering cost and carrying cost are 10% lower than originally;estimated.(b) both ordering cost and carrying cost are 10% higher than;originally estimated, (c) ordering cost is 10% higher and carrying cost is 10%;lower than originally estimated, (d) ordering cost is 10% lower and carrying;cost is 10% higher than originally estimated.;Determine;the optimal order quantity and total inventory cost for each of the four cases.;Prepare a;table with values from all four cases and compare the sensitivity of the model;solution to changes in parameter values.;problem 4;The;Western Jeans Company purchases denim from Cumberland Textile Mills. The;Western Jeans Company uses 235,000 yards of denim per year to make jeans. The;cost of ordering denim from the textile company is $250 per order. It costs;Western $1.65 per yard annually to hold a yard of denim in inventory. Determine;the optimal number of yards of denim the Western Jeans Company should order;the minimum total annual inventory cost, the optimal number of orders per year;and the optimal time between orders.;If;possible, use Excel 3M or QM for Windows.;Module 5;Chapter;Problems;7;6, 13, 17;Module 6;Chapter;Problems;8;2, 6, 12;9;22, 24;For the;module assignment, you must complete the problems below from your textbook;For the;Chapter 8 questions, answer part A only for each.;For 9-24;you must provide a solution for the problem that shows how you obtained your;answers and specific answers to the questions.;2. A company produces two products that are processed on two;assembly lines. Assembly line 1 has 100 available hours, and assembly line 2;has 42 available hours. Each product requires 10 hours of processing time on;line 1, while on line 2 product 1 requires 7 hours and product 2 requires 3;hours. The profit for product 1 is $6 per unit, and the profit for product 2 is;$4 per unit.;a. Formulate a linear programming model for this problem.;b. Solve the model by using graphical analysis.;6. The Pinewood Furniture Company produces chairs and tables from two resources;? labor and wood. The company has 80 hours of labor and 36 board-ft. of wood;available each day. Demand for chairs is limited to 6 per day. Each chair;requires 8 hours of labor and 2 board-ft. of wood, whereas a table requires 10;hours of labor and 6 board-ft. of wood. The profit derived from each chair is;$400 and from each table, $100. The company wants to determine the number of;chairs and tables to produce each day in order to maximize profit. Formulate a;linear programming model for this problem.;a. Formulate a linear programming model for this problem.;b. Solve the model by using graphical analysis.;12. The Elixer Drug Company produces a drug from two ingredients. Each;ingredient contains the same three antibiotics, in different proportions. One;gram of ingredient 1 contributes 3 units and one gram of ingredient 2;contributes 1 unit of antibiotic 1, the drug requires 6 units. At least 4 units;of antibiotic 2 are required and the ingredients contribute 1 unit each per;gram. At least 12 units of antibiotic 3 are required, a gram of ingredient 1;contributes 2 units, and a gram of ingredient 2 contributes 6 units. The cost;for a gram of ingredient 1 is $80, and the cost for a gram of ingredient 2 is;$50. The company wants to formulate a linear programming model to determine the;number of grams of each ingredient that must go into the drug in order to meet;the antibiotic requirements at the minimum cost.;a. Formulate a linear programming model for this problem.;b. Solve the model by using graphical analysis.;Module 7.Betty Malloy, owner of the Eagle Tavern in Pittsburgh, is preparing for;Super Bowl Sunday, and she must determine how much beer to stock.Betty stocks;three brands of beer - Yodel, Shotz, and Rainwater.The cost per gallon (to the;tavern owner) of each brand is as follows;Brand Cost/gallon;Yodel $1.50;Shotz 0.90;Rainwater 0.50;The tavern has a budget of $2,000 for beer for Super Bowl Sunday.Betty sells;Yodel at a rate of $3.00 per gallon, Shotz at $2.50 per gallon, and Rainwater;at $1.75 per gallon.Based on past football games, Betty has determined the;maximum customer demand to be 400 gallons of Yodel, 500 gallons of Shotz, and;300 gallons of Rainwater.The tavern has a capacity to stock 1,000 gallons of;beer, Betty wants to stock up completely.Betty wants to determine the number;of gallons of each brand of beer to order so as to maximize profit.;a. Formulate a linear programming model for this problem (written in a;format similar to the way Problems 1 and 2 were presented).;b. Solve this problem by using the computer.;3. Joe Henderson runs a small metal part shop. The shop contains three;machines- a drill press, a lathe, and a grinder. Joe has three operators, each;certified to work on all three machines. However each operator performs better;on some machines than on other. The shop has contracted to do a big job that;requires all three machines. The times required by the various operators to;perform the required operations on each machine are summarized as follows.;Operator Drill Press (min) Lathe (min) Grinder (min);1 22 18 35;2 41 30 28;3 25 36 18;Joe Henderson wants to assign one operator to each machine so that the total;operating time for all three operators in minimized.;A. Formulate a linear programming model for this problem;B. Solve the model using the computer;C. Joe's brother, Fred, has asked him to hire his wife, Kelly, who is a machine;operator. Kelly can perform each of the three required machine operations in 20;minutes. Should Joe hire his sister-in-law?;16. The athletic boosters club for Beaconville has planned a 2-day;fund-raising drive to purchase uniforms for al the local high schools and to;improve facilities. Donations will be solicited during the day and night by;telephone and personal contact. The boosters club has arranged for local;college students to donate their time to solicit donations. The average;donation from each type of contact and the time for a volunteer to solicit each;type of donations are as follows;Average donation ($) Average Interview Time (min.);Phone Personal Phone Personal;Day 16 33 6 13;Night 17 37 7 19;The boosters club has gotten several businesses and car dealers to donate;gasoline and cars for the college students to use to make a maximum of 575;personal contacts daily during the fund-raising drive. The college students;will donate a total of 22 hours during the day and 43 hours at night during the;drive.;The president of the booster club wants to know how many different types of;donor contacts to schedule during the drive to maximize the total donations.;Formulate and solve an integer program between the integer and non-integer;rounded-down solutions to this problem?;Harry and Melissa Jacobson produce handcrafted furniture in a workshop on;their farm. They have obtained a load of 600 board feet of birch from a;neighbor and are planning to produce round kitchen tables and ladder-back;chairs during the next 3 months. Each table will require 30 hours of labor;each chair will require 18 hours, and between them they have a total of 480;hours of labor available. A table requires 40 board feet of wood to make, and a;chair requires 15 board feet. A table earns the couple $575 in profit. Most;people who buy a table also want four chairs to go with it, so for every table;that is produced, at least four chairs must also be made, although additional;chairs can also be sold separately. Formulate and solve an integer programming;model to determine the number of tables and chairs the Jacobsons should make to;maximize profit.
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