Answer:
They should operate Mine 1 for 1 hour and Mine 2 for 3 hours to meet the contractual obligations and minimize cost.
Explanation:
The formulation of the linear programming is:
Objective function:
[tex]C=200M_1+160M_2[/tex]
Restrictions:
- High-grade ore: [tex]6M_1+2M_2\geq12[/tex]
- Medium-grade ore: [tex]2M_1+2M_2\geq8[/tex]
- Low-grade ore: [tex]4M_1+12M_2\geq24[/tex]
- No negative hours: [tex]M_1,M_2\geq0[/tex]
We start graphing the restrictions in a M1-M2 plane.
In the figure attached, we have the feasible region, where all the restrictions are validated, and the four points of intersection of 2 restrictions.
In one of this four points lies the minimum cost.
Graphically, we can graph the cost function over this feasible region, with different cost levels. When the line cost intersects one of the four points with the lowest level of cost, this is the optimum combination.
(NOTE: it is best to start with a low guessing of the cost and going up until it reaches one point in the feasible region).
The solution is for the point (M1=1, M2=3), with a cost of C=$680.
The cost function graph is attached.
