First formulate problems $1$ and $2$ as an LP problem.

b$.$ For all problems, determine the feasible region.

c$.$ For all problems determine all the corner points of the feasible region.

d$.$ For all problems, determine the optimal solution and objective function value.

e$.$ For all problems identify the binding constraints.

$1.$ Ebel Mining Company owns two different mines that produce a given kind of ore. The mines

are located in different parts of the country and hence have different production quantities and

ore qualities. After crushing the ore is graded into $3$ classes: high grade, medium grade and

low grade. Ebel has contracted to provide it$$s parent company with $12$ tons of high grade, $8$

tons of medium grade and $24$ tons of low grade ore per week. It costs Ebel $$20,000$ per day to

run the first mine and $$16000$ per day to run the second. However, in a day$$s operation, the

first mine produces $6$ tons of high grade, $2$ tons of medium grade and $4$ tons of low grade ore.

The second produces $2$ tons of high and medium grade per day and $12$ tons of low grade ore.

How many days a week should each mine be operated to fulfill Ebel$$s commitment most

economically?