# The Copperfield Mining Company owns two mines, which produce three grades of ore: high, medium, and low. It cost Copperfield \$200 per hour to mine ore from mine 1, and

The Copperfield Mining Company owns two mines, which produce three grades of ore: high, medium, and low. It cost Copperfield \$200 per hour to mine ore from mine 1, and it cost \$160 per hour to mine ore from mine 2. The company developed the following mathematical model to determine the number of hours it needs to operate each mine so that its contractual obligations can be met at the lowest. Using the graphical analysis, the company found point B as the optimal solution. Min 200×1 + 160×2 (cost, \$) Subject to: 6×1 + 2X2 >= 12 (high-grade ore tons) 2×1 + 2X2 >= 8 (medium-grade ore tons) 4×1 + 12×2 >= 24 (low-grade ore tons) X1, x2 ≥ 0 a, Identify the sensitivity ranges for the objective function coefficients b, Identify the sensitivity ranges for the right hand values of the first and third constriants SEE ATTACHMENT FOR ADDITIONAL GRAPH. PLEASE SHOW ALL WORKING, NO SOFTWARE