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Question;Homework 3;Supplemented Questions;1. Consider the following linear program:..;3 +;2;1 +;1? 10;3 +;1? 24;1;+ 2? 16,? 0;a. Use the graphical solution procedure to find the;optimal solution.;b.;Assume that;the objective function coefficient for A changes from 3 to 5. Does the optimal;solution change? Use the graphical solution procedure to find the new optimal;solution.;c.;Assume that;the objective function coefficient for A remains 3, but the objective function;coefficient for B changes from 2 to 4. Does the optimal solution change? Use;the graphical solution procedure to find the new optimal solution.;d. The computer solution for the linear program in;part (a) provides the following objective coefficient range information;Objective;Allowable;Allowable;Variable;Coefficient;Increase;Decrease;A;3.00000;3.00000;1.00000;B;2.00000;1.00000;1.00000;Use this objective coefficient range information to answer parts (b) and;(c);Quantitative;Analysis BA 452 Homework 3 Questions;2.;Consider;the linear program in Problem 1. The value of the optimal solution is 27.;Suppose that the right-hand side for constraint 1 is increased from 10 to 11.;a. Use the graphical solution procedure to find the;new optimal solution.;b. Use the solution to part (a) to determine the;dual value or constraint 1.;c. The computer solution for the linear program in;Problem 1 provides the following right-hand-side range information;RHS;Allowable;Allowable;Constraint;Value;Increase;Decrease;1;10.00000;1.20000;2.00000;2;24.00000;6.00000;6.00000;3;16.00000;Infinite;3.00000;d. The dual value for constraint 2 is 0.5. Using;this dual value and the right-hand-side range information in part (c), what;conclusion can be drawn about the effect of changes to the right-hand side of;constraint 2?;Quantitative;Analysis BA 452 Homework 3 Questions;3.;Consider;the following linear program;Min;8X + 12Y;s.t.;1X;+ 3Y;? 9;2X;+ 2Y;? 10;6X;+ 2Y;? 18;A, B? 0;a. Use the graphical solution procedure to find the;optimal solution.;b.;Assume that;the objective function coefficient for X changes from 8 to 6. Does the optimal;solution change? Use the graphical solution procedure to find the new optimal;solution.;c.;Assume that;the objective function coefficient for S remains 8, but the objective function;coefficient for Y changes from 12 to 6. Does the optimal solution change? Use;the graphical solution procedure to find the new optimal solution.;d.;The;computer solution for the linear program in part (a) provides the following;objective coefficient range information;Objective;Allowable;Allowable;Variable;Coefficient;Increase;Decrease;X;8.00000;4.00000;4.00000;Y;12.00000;12.00000;4.00000;How would this objective coefficient range;information help you answer parts (b) and (c) prior to re-solving the problem?;Quantitative;Analysis BA 452 Homework 3 Questions;4.;Consider;the linear program in Problem 3. The value of the optimal solution is 48.;Suppose that the right-hand side for constraint 1 is increased from 9 to 10.;a. Use the graphical solution procedure to find the;new optimal solution.;b. Use the solution to part (a) to determine the;dual value for constraint 1.;c.;The;computer solution for the linear program in Problem 3 provides the following;right-hand-side range information;RHS;Allowable;Allowable;Constraint;Value;Increase;Decrease;1;9.00000;2.00000;4.00000;2;10.00000;8.00000;1.00000;3;18.00000;4.00000;Infinite;What does the right-hand-side range information;for constraint 1 tell you about the dual value for constraint 1?;d.;The dual;value for constraint 2 is 3. Using this dual value and the right-hand-side;range information in part (c), what conclusion can be drawn about the effect of;changes to the right-hand side of constraint 2?;Quantitative;Analysis BA 452 Homework 3 Questions;5.;Refer to;the Kelson Sporting Equipment problem (Chapter 2, Problem 24). Letting;R=number of regular gloves C=number of catcher?s;mitts;Leads to the following formulation;5;+ 8..;+?32?? 900?12?+?13??300?;?18? +?14?? 100?,? 0;The computer solution is shown I Figure 3.13.;Quantitative;Analysis BA 452 Homework 3 Questions;a.;What is the optimal solution, and what is the value of the total;profit contribution?;b. Which constraints are binding?;c. What are the dual values for the resources?;Interpret each.;d.;If overtime;can be scheduled in one of the departments, where would you recommend doing so?;6.;Refer to;the computer solution of the Kelson Sporting Equipment problem in Figure 3.13;(see Problem 5).;a. Determine the objective coefficient ranges.;b. Interpret the ranges in part (a).;c. Interpret the right-hand-sides ranges.;d.;How much;will the value of the optimal solution improve if 20 extra hours of packaging;and shipping time are made available?;Quantitative;Analysis BA 452 Homework 3 Questions;7.;Investment;Advisors, Inc., is a brokerage firm that manages stock portfolios for a number;of clients. A particular portfolio consists of U shares of U.S. Oil and H;shares of Huber Steel. The annual return for U.S. Oil is $3 per share and the;annual return for Huber Steel is $5 per share. U.S. Oil sells for $25 per share;and Huber Steel sells for $50 per share. The portfolio has $80,000 to be;invested. The;portfolio risk index (.50 per share of U.S. Oil;and 0.25 per share for Huber Steel) has a maximum of 700. In addition, the;portfolio is limited to a maximum of 1000 shares of U.S. Oil. The linear;programming formulation that will maximize the total annual return of;the portfolio is as follows;3 +;5..;25 +;50? 80,000;0.50 + 0.25?;700;1;?;0;?;1000..;The computer solution of this problem is shown in Figure 3.14.;Quantitative Analysis;BA 452 Homework 3 Questions;a. What is the optimal solution, and what is the;value of the total annual return?;b.;Which;constraints are binding? What is your interpretation of these constraints in;terms of the problem?;c. What are the dual values for the constraints?;Interpret each.;d. Would it be beneficial to increase the maximum;amount invested in U.S. Oil? Why or why not?

 

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