Chapter06S - SUPPLEMENT TO CHAPTER 6 LINEAR PROGRAMMING...

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SUPPLEMENT TO CHAPTER 6: LINEAR PROGRAMMING Teaching Notes The main goal of this supplement is to provide the students with an overview of the types of problems that have been solved using linear programming (LP). In the process of learning the different types of problems that can be solved with LP, the students must also develop a very basic understanding of the assumptions and special features of LP problems. The students should also learn the basics of developing and formulating linear programming models for simple problems, solve two-variable linear programming problems by the graphical procedure and interpret the resulting outcome. In the process of solving these graphical problems, we must stress the role and importance of extreme points in obtaining an optimal solution. The improvements in computer hardware and software technology and popularity of the software package Microsoft Excel makes the use of computers in solving linear programming problems accessible to many users. Therefore, a main goal of the chapter should be to allow students to solve linear programming problems using Excel. More importantly, we need to make sure that the students are able to interpret the results obtained from Excel or any another computer software package. Answers to Discussion and Review Questions 1. Linear programming is well-suited to an environment of certainty. 2. The “area of feasibility,” or feasible solution space is the set of all combinations of values of the decision variables which satisfy the constraints. Hence, this area is determined by the constraints. 3. Redundant constraints do not affect the feasible region for a linear programming problem. Therefore, they can be dropped from a linear programming problem without affecting the optimal solution. 4. An iso-cost line represents the set of all possible combinations of two inputs that will result in a given cost. Likewise, an iso-profit line represents all of the possible combinations of two outputs which will yield a given profit. 5. Sliding an objective function line towards the origin represents a decrease in its value (i.e., lower cost, profit, etc.). Sliding an objective function line away from the origin represents an increase in its value. 6. a. Basic variable : In a linear programming solution, it is a variable not required to equal zero. b. Shadow price : It is the change in the value of the objective function per unit increase in a constraint right hand side. c. Range of feasibility : The range of values over which a constraint’s right hand side value may vary without changing the optimal basic feasible solution. d. Range of optimality : The range of values over which a variable’s objective function value may vary without changing the current optimal basic feasible solution.
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