Exercise $17-21$ Algo

Consider the following LP problem.

Minimize z $=7$x$1+5$x$2+5$x$3,$

Subject to

Constraint $1$: $7$x$1+6$x$2+4$x$3>=50,$

Constraint $2$: $10$x$1+13$x$2+14$x$3>=150,$

Constraint $3$: x$1,$x$2,$x$3>=0,$

where x$1,$ x$2,$ and x$3$ represent the decision variables. Solve the LP problem to answer the following questions.

a$-1.$ What are the values of x$1,$ x$2,$ and x$3$ at the optimal solution?

Note: Round your answers to $2$ decimal places.

a$-2.$ What is the minimum value of z$?$

Note: Round your answers to $2$ decimal places.

b$.$ Identify the binding and nonbinding constraints and report the surplus value, as appropriate.

Note: If the answer to constraints is "Non$-$Binding" enter surplus value to $2$ decimal places or leave cells blank.

c$.$ Report the values and ranges of feasibility of the shadow price of each binding constraint. Interpret the results.

Note: Round your answers to $2$ decimal places.

d$.$ What is the range of optimality for the three objective function coefficients? Interpret the results.

Note: Round your answers to $2$ decimal places.