Answer to Question #236167 in Operations Research for Bebe

Question

The Copper Mining company owns 2 mines, which produce 3 grades of ore - high, medium, and low. The company has a contract to supply a smelting company with 12 tons of high-grade ore, 8 tons of medium-grade ore, and 24 tons of low-grade ore. Each mine produces a certain amount of each type of ore each hour it is in operation. The company has developed the following LP model to determine the number of hours to operate each mine X and Y so that contractual obligations can be met at the lowest cost.

Answer 1

Solution:

Let x₁ = the number of hours that mine 1 operates,

And x₂ = the number of hours that mine 2 operates

Constraint functions are:

$x_1 \ge0 \\x_2\ge 0 \\6x_1 + 2x_2 \ge 12\Rightarrow 3x_1+x_2\ge6 \\2x _1+ 2x_2 \ge8\Rightarrow x_1+x_2\ge4 \\4x_1 + 12x_2 \ge 24\Rightarrow x_1+3x_2\ge6$

Minimise cost, $C=200x_1+160x_2$

After introducing slack,surplus,artificial variables:

Similarly, doing this process to 4-iteration,

we get, optimal solution is arrived with value of variables as :

$x_1=1,x_2=3$

Min Z=$680