Consider the following LP problem. Minimize

$$

$=$

$6$

$$

$1$

$+$

$6$

$$

$2$

$+$

$6$

$$

$3$

$$Subject

$$

$$

$$Constraint

$1$

:

$7$

$$

$1$

$+$

$6$

$$

$2$

$+$

$4$

$$

$3$

$>=$

$5$

$0$

$$Constraint

$2$

:

$1$

$0$

$$

$1$

$+$

$1$

$3$

$$

$2$

$+$

$1$

$4$

$$

$3$

$>=$

$1$

$5$

$0$

$,$

$$Constraint

$3$

:

$$

$1$

$,$

$$

$2$

$,$

$$

$3$

$>=$

$0$

$$where

$$

$1$

$,$

$$

$2$

$,$

$$and

$$

$3$

$$represent the decision variables. Solve the LP problem to answer the following questions.

$0$

$-$

$1$

$.$

$$What are the values of

$$

$1$

$,$

$$

$2$

$,$

$$and

$$

$3$

$$at the optimal solution? Note: Round your answers to

$2$

$$decimol places.

$\backslash$

table

$[$

$[$

$$

$1$

$,$

$]$

$,$

$[$

$$

$2$

$,$

$]$

$,$

$[$

$$

$3$

$,$

$]$

$]$

$$a

$-$

$2$

$.$

$$What is the minimum value of

$$

$?$

$$Note: Round your answers to

$2$

$$decimol places.

$$

$$b

$.$

$$Identify the binding and nonbinding constraints and report the surplus value, as appropriate. Note: If the answer to constralnts is "Non

$-$

BInding" enter surplus value to

$2$

$$declmal places or leave cells blank.

$\backslash$

table

$[$

$[$

Constraint

$1$

$,$

$,$

$]$

$,$

$[$

Constraint

$2$

$,$

$,$

$]$

$]$

$$c

$.$

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