$($Please solve part c and d using excel solver sensitive report.

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 right.

The company has contrasted 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

$$6,000$ per day to operate mill I and $$7,000$ per day to operate mill $2.$ The company wants to know

the number of days to operate each mill to meet the contract at the minimum cost.

a$.$ Formulate a linear programming model for this problem.

b$.$ Solve this model by using graphical analysis.

c$.$ Identify the sensitivity ranges for the objective function coefficients

d$.$ Identify the sensitivity ranges for the constraint quantity values.