Question;Quantitative Analysis;BA 452 Homework 3 Questions;19.;Better;Products, Inc., manufactures three products on two machines. In a typical week;40 hours are available on each machine. The profit contribution and production;time in hours per unit are as follows;Category;Product 1;Product 2;Product 3;Profit/unit;$30;$50;$20;Machine 1 time/unit;0.5;2.0;0.75;Machine 2;time/unit;1.0;1.0;0.5;Two operators are required for machine 1, thus, 2;hours of labor must ne scheduled for each hour of machine 1 time. Only one;operator is required for machine 2. A maximum of 100 labor-hours is available;for assignment to the machines during the coming week.;Other production requirements are that product 1;cannot account for more than 50% of the units produced and that product 3 must;account for at least 20% of the units produced.;a. How many units of each product should be produced;to maximize the total profit contribution? What is the projected weekly profit;associated with your solution?;b. How many hours of production time will be;scheduled on each machine?;c. What is the value of an additional hour of labor?;d.;Assume that;labor capacity can be increased to 120 hours. Would you be interested in using;the additional 20 hours available for this resource? Develop the optimal;product mix assuming the extra hours are made available.;20.;Adirondack;Savings Bank (ASB) has $1 million in new funds that must be allocated to home;loans, personal loans, and automobile loans. The annual rates of return for the;three types of loans are 7% for home loans, 12% for personal loans, and 9% for;automobile loans. The bank?s planning committee has decided that at least 40%;of new funds must be allocated to home loans. In addition, the planning;committee has specified that the amount allocated to personal loans cannot;exceed 60% of the amount allocated to automobile loans.;a.;Formulate a;linear programming model that can be used to determine the amount of finds ASB;should allocate to each type of loan in order to maximize the total annual;return for the new funds.;b. How much should be allocated to each type of;loan? What is the total annual return? What is the annual percentage return?;c. If the interest rate on home loans increased to;9%, would the amount allocated to each type of loan change? Explain.;d. Suppose the total amount of new funds available;was increased by $10,000. What effect would this have on the total annual;return? Explain.;e.;Assume that;ASB has the original $1 million in new funds available and that the planning;committee has agreed to relax the requirement that at least 40% of the new;funds must be allocated to home loans by 1%. How much would the annual return;change? How much would the annual percentage return change?;Quantitative;Analysis BA 452 Homework 3 Questions;21.;Round Tree;Manor is a hotel that provides two types of rooms with three rental classes;Super Saver, Deluxe, and Business. The profit per night for each type of room;and rental class is as follows;Room;Super Saver;Deluxe;Business;Type I;$30;$35;--;Type II;$20;$30;$40;Type I rooms do not have Internet access and are not available for the;Business rental class.;Round Tree?s;management makes a forecast of the demand by rental class for each m=night in;the future. A linear programming model developed to maximize profit is used to;determine how many reservations to accept for each rental class. The demand;forecast for a particular night is 130 rentals in the Super Saver class, 60;rental sin the Deluxe class, and 50 rentals in the Business class. Round Tree;has 100 Type I rooms and 120 Type II rooms.;a.;Use linear;programming to determine how many reservations to accept in each rental class;and how the reservations should be allocated to room types. Is the demand by;any rental class not satisfied? Explain.;b. How many reservations can be accommodated in each;rental class?;c.;Management;is considering offering a free breakfast to anyone upgrading from a Super Saver;reservation to Deluxe class. If the cost of the breakfast to Round Tree is $5.;Should this incentive be offered?;d.;With a;little work, an unused office area could be converted to a rental room. If the;conversion cost is the same for both types of rooms, would you recommend;converting the office to a Type I or a Type II room? Why?;e.;Could the;linear programming model be modified to plan for the allocation of rental;demand for the next night? What information would be needed and how would the;model change?;Quantitative;Analysis BA 452 Homework 3 Questions;22.;Industrial Design has been awarded a contract;design label for a new wine produced by Lake View Winery. The company estimates;that 150 hours will be required to complete the project. The firm?s three;graphics designers available for assignment to this project are Lisa, a senior;designer and team leader, David, a senior designer, and Sarah, a junior;designer. Because Lisa has worked on several projects for Lake View Winery;management specified that Lisa must be assigned at least 40% of the total;number of hours assigned to the two senior designers. To provide;label-designing experience for Sarah, Sarah must be assigned at least 15% of;the total project time. However, the total number of hours assigned to Sarah;must not exceed 25% of the total number of hours assigned to the two senior;designers. Due to other project commitments, Lisa has a maximum of 50 hours;available to work on this project. Hourly wage rates are $30 for Lisa, $25 for;David, and $18 for Sarah.;a. Formulate a linear program that can be used to;determine the number of hours each graphic designer should be assigned to the;project in order to minimize total cost.;b.;How many;hours should each graphic designer be assigned to the project? What is the;total cost?;c.;Suppose;Lisa could be assigned more than 50 hours. What effect would this have on the;optimal solution? Explain.;d. If Sarah were not required to work a minimum;number of hours on this project, would the optimal solution change? Explain.;23.;Vollmer;Manufacturing makes three components for sale to refrigeration companies. The;components are processed on two machines: a sharper and a grinder. The times;(in minutes) required on each machine are as follows;Machine;Component;Sharper;Grinder;1;6;4;2;4;5;3;4;2;The sharper is available for 120 hours, and the grinder is available;for 110 hours. No more than 200 units of component 3 can be sold, but up to;1000 units of each of the other components can be sold. In fact, the company;already has orders for 600 units of component 1 that must be satisfied. The;profit contributions for components 1,2, and 3 are $8, $6, and $9;respectively.;a. Formulate and solve for the recommended;production quantities.;b.;What are;the objective coefficient ranges for the three components? Interpret these;ranges for company management.;c. What are the right-hand-side ranges? Interpret;these ranges for company management.;d. If more time could be made available on the;grinder, how much would it be worth?;e. If more units of component 3 can be sold by;reducing the sales price by $4, should the company reduce the price?;Quantitative;Analysis BA 452 Homework 3 Questions;24.;National;Insurance Associates carries an investment portfolio of stocks, bonds, and;other investment alternatives. Currently $200,000 of funds are available and;must be considered fro new investment opportunities. The four stock options;National is considering and the relevant financial data are as follows;Stock;A;B;C;D;Price per share;$100;$50;$80;$40;Annual rate of return;0.12;0.08;0.06;0.10;Risk measure per dollar;0.10;0.07;0.05;0.08;invested;The risk measure indicates the relative;uncertainty associated with the stock in terms of it realizing the projected;annual return, higher values indicate greater risk. The risk measures are;provided by the firm?s top financial advisor.;National?s top;management has stipulated the following investment guidelines: The annual rate;of return for the portfolio must be at least 9% and o one stock can account of;more than 50% of the total dollar investment.;a. Use linear programming to develop an investment;portfolio that minimizes risk.;b.;If the firm;ignores risk and uses a maximum return-on-investment strategy, what is the;investment portfolio?;c.;What is the;dollar difference between the portfolios in parts (a) and (b)? Why might the;company prefer the solution developed in part (a)?;Quantitative;Analysis BA 452 Homework 3 Questions;25.;Georgia;Cabinets manufactures kitchen cabinets that are sold to local dealers;throughout the Southeast. Because of a large backlog of orders for oak and;cherry cabinets, the company decided to contract with three smaller;cabinetmakers to do the final finishing operation. For the three cabinetmakers;the number of hours required to complete all the oak cabinets, the number of;hours required to complete all the cherry cabinets, the number of hours;available for the final finishing operation, and the cost per hour to perform;the work are shown here.;Cabinetmaker 1;Cabinetmaker 2;Cabinetmaker 3;Hours required to;50;42;30;complete all the;oak cabinets;Hours required to;60;48;35;complete all the;cherry cabinets;Hours available;40;30;35;Cost per hour;$36;$42;$55;For example, Cabinetmaker 1 estimates it will;take 50 hours to complete all the oak cabinets and 60 hours to complete all the;cherry cabinets. However, Cabinetmaker 1 only has 40 hours available for the;final finishing operations. Thus, Cabinetmaker 1 can only complete 40/50 =;0.80, or 80%, of the oak cabinets if it worked only on oak cabinets. Similarly;Cabinetmaker 1 can only complete 40/60 = 0.67, or 67%, of the cherry cabinets;if it worked only on cherry cabinets.;a.;Formulate a;linear programming model that can be used to determine the percentage of the;oak cabinets and the percentage of the cherry cabinets that should be given to;each of the three cabinetmakers in order to minimize the total cost of;completing both projects.;b.;Solve the;model formulated in part (a). What percentage of the oak cabinets and what;percentage of the cherry cabinets should be assigned to each cabinetmaker? What;is the total cost of completing both projects?;c. If Cabinetmaker 1 has additional hours available;would the optimal solution change? Explain.;d.;If;Cabinetmaker 2 has additional hours available, would the optimal solution;change? Explain.;e.;Suppose;Cabinetmaker 2 reduced its cost to $38 per hour. What effect would this change;have on the optimal solution? Explain.;Quantitative;Analysis BA 452 Homework 3 Questions;26.;Benson;Electronics manufactures three components used to produce cell telephones and;other communication devices. In a given production period, demand for the three;components may exceed Benson?s manufacturing capacity. Tin this case, the;company meets demand by purchasing the components from another manufacturer at an;increased cost per unit. Benson?s manufacturing cost per unit and purchasing;cost per unit for the three components are as follows;Source;Component;1;Component;2;Component 3;Manufacture;$4.50;$5.00;$2.75;Purchase;$6.50;$8.80;$7.00;Manufacturing times in minutes per unit for Benson?s three departments;are as follows;Department;Component 1;Component 2;Component;3;Production;2;3;4;Assembly;1;1.5;3;Testing;Packaging;1.5;2;5;For instance, each unit for component 1 that Benson manufactures;requires 2 minutes of production time, 1 minute of assembly time, and 1.5;minutes of testing and packaging time. For the next production period, Benson;has capacities of 360 hours in the production department, 250 hours in the;assembly department, and 300 hours in the testing and packaging department.;a.;Formulate a;linear programming model that can be used to determine how many units of each;component to manufacture and how many units of each component to purchase.;Assume that component demands that must be satisfied are 6000 units for;component 1, 4000 units for component 2, and 3500 units for component 3. The;objective is to minimize the total manufacturing and purchasing costs.;b.;What is the;optimal solution? How many units of each component should be manufactured and;how many units of each component should be purchased?;c. Which departments are limiting Benson?s;manufacturing quantities? Use the dual value to determine the value of an extra;hour in each of these departments.;d.;Suppose;that Benson had to obtain one additional unit of component 2. Discuss what the;dual value for the component 2 constraints tells us about the cost to obtain;the additional unit.
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