Homework Exercises

Use some optimization software to solve the following LP and obtain the Sensitivity Report.

Maximize $P=20x_1+16x_2+10x_3$

subject $to$ constrain $14$x$1$

Homework Exercises

Use some optimization software to solve the following LP and obtain the Sensitivity Report.

Maximize $P=20x_1+16x_2+10x_3$

subject $to$ Constraint $1,4x_1+2x_2+3x_{3}120$

Constraint $2_5{x}_1+4x_2+2x_{3}100$

Constraint $3,2x_1+3x_2+3x_{3}90$

where $xis$ non$-$negative

a$)$ Which variables are in the optimal basis? What are their optimal values?

b$)$ Which constraints have excess capacity in the optimal solution? How many units of each can be sold off without impacting the optimal solution?

c$)$ What are the reduced costs of the non$-$basic variables?

d$)$ If one could increase the right$-$hand side of one of the constraints by one unit, which constraint has the best one to increase, Constraint $1,2$ or $3?$

e$)$ If one could increase just one of the objective coefficients by one, which coefficient is the best one to increase $x_1,x_2,x_1$ or $x_4?$

a$)$ Which variables are in the optimal basis? What are their optimal values?

b$)$ Which constraints have excess capacity in the optimal solution? How many units of each can be sold off without impacting the optimal solution?

c$)$ What are the reduced costs of the non$-$basic variables?

d$)$ If one could increase the right$-$hand side of one of the constraints by one unit, which constraint has the best one to increase, Constraint $1,2$ or $3?$

e$)$ If one could increase just one of the objective coefficients by one, which coefficient is the best one to increase $x_1,x_2,x_1$ or $x_1?$