Exercise $18-1$ Static

Consider the following IP problem.

Maximize $z=3x_1+2x_2,$

subject to

Constraint $1$: $,2x_1+3x_{2}40,$

Constraint $2$: $3x_1+x_{2}30,$

Constraint $3$: $x_1,x_{2}0,$

constraint $4$: $,x_1,x_2=$ non$-$negative integer,

where $x_1$ and $x_2$ represent the decision variables. Solve this IP problem and answer the following questions.

a$.$ What are the values of $x_1$ and $x_2$ at the optimal solution? What is the maximum value of $z?$

b$.$ If the objective function coefficients change to $z=4x_1+3x_2,$ what are the values of $x_1$ and $x_2$ at the optimal solution? What is the

maximum value of $z?$

c$.$ Using the original objective function coefficients, if the first constraint changes to $2x_1+3x_{2}47,$ what are the values of $x_1$ and $x_2$ at

the optimal solution? What is the maximum value of $z?$