A$)$ United Aluminum Company of Cincinnati produces three grades $($high$,$ medium, and low$)$ of aluminum at two mills. Each mill has a different production capacity $($in tons per day$)$ for each grade, as shown below. The company has contracted with a manufacturing firm to supply at least $12$ tons of high$-$grade aluminum, $8$ tons of medium$-$grade aluminum, and $5$ tons of low$-$grade aluminum. It costs United $$6,000$ per day to operate mill $1$ and $$7,000$ per day to operate mill $2.$ The company wants to know the number of days to operate each mill in order to meet the contract at the minimum cost. Formulate a linear programming model for this problem. Define x$1$ as the number of operation days for mill $1,$ x$2$ as the number of operation days for mill $2,$ and Z as the total cost. Which of the following model formulations is correct?Solve the previous formulated model $($United Aluminum Company$)$ by using Excel and POM$-$QM$,$ the sensitivity range for objective function coefficient of x$1($or mill $1),$ is

Group of answer choices

$[1000,6000]$

$[6000,$ infinite$]$

$[0,7000]$

$[-6000,0]$