1. JBap is a student in the ECON 3037 class. She realizes that all work and...

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1. JBap is a student in the ECON 3037 class. She realizes that "all work and no play makes JBap a dull girl." She decides to create an LP model to maximize her pleasure from both work and play. Her decision variables are x1 = Play hours per day x2 = Work hours per day She estimates that play is twice as fun as work and comes up with the following objective function: z = 2x1 + x2 JBap has a total of 10 hours a day available to her to apportion between work and play. She also wants to study, that is, work at least as much as she plays. Finally, she realizes that if she is going to get all her homework assignments done, she cannot play more than 4 hours a day. (i) Write down JBap's complete LP model. [4] (ii) Solve the LP model graphically to determine how JBap should allocate her time. (iii) Indicate which constraints are binding. [7] [1] 2. The following tableau represents a specific simplex iteration. All variables are nonnegative. The tableau is not optimal for either a maximization or a minimization problem. Basic Variable No. Row Coefficient of Right Z X1 x2 X3 x4 X5 S1 S2 S3 Side Z S3 11 1 00 00 -5 0 4 -1 -10 0 0 620 3 0 -2 -3 -1 5 1 12 X3 x1 2 00 1 1 3 1 0 3 0 6 3 01 -1 0 0 6 -4 0 0 0 (i) (ii) (iii) Categorize the variables as basic and non - basic and provide the current values of all the variables. [4] Assuming that the problem is of the maximization type, identify the non- basic variables that have the potential to improve the value of z. If each such variable enters the basic solution, determine the associated leaving variable, if any, and the associated change in z. Do not use Gauss - Jordan row operations. [7] Repeat part (b) assuming that the problem is of the minimization type. [2] 1. JBap is a student in the ECON 3037 class. She realizes that "all work and no play makes JBap a dull girl." She decides to create an LP model to maximize her pleasure from both work and play. Her decision variables are x1 = Play hours per day x2 = Work hours per day She estimates that play is twice as fun as work and comes up with the following objective function: z = 2x1 + x2 JBap has a total of 10 hours a day available to her to apportion between work and play. She also wants to study, that is, work at least as much as she plays. Finally, she realizes that if she is going to get all her homework assignments done, she cannot play more than 4 hours a day. (i) Write down JBap's complete LP model. [4] (ii) Solve the LP model graphically to determine how JBap should allocate her time. (iii) Indicate which constraints are binding. [7] [1] 2. The following tableau represents a specific simplex iteration. All variables are nonnegative. The tableau is not optimal for either a maximization or a minimization problem. Basic Variable No. Row Coefficient of Right Z X1 x2 X3 x4 X5 S1 S2 S3 Side Z S3 11 1 00 00 -5 0 4 -1 -10 0 0 620 3 0 -2 -3 -1 5 1 12 X3 x1 2 00 1 1 3 1 0 3 0 6 3 01 -1 0 0 6 -4 0 0 0 (i) (ii) (iii) Categorize the variables as basic and non - basic and provide the current values of all the variables. [4] Assuming that the problem is of the maximization type, identify the non- basic variables that have the potential to improve the value of z. If each such variable enters the basic solution, determine the associated leaving variable, if any, and the associated change in z. Do not use Gauss - Jordan row operations. [7] Repeat part (b) assuming that the problem is of the minimization type. [2]