The Copperfield Mining Company owns two mines, which produce three 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 linear programming model to determine the number of hours to operate each mine (x1 and x2) so that contracted obligations can be met at the lowest cost:
Minimize Z = 200x1 + 160x2 1cost, $2
Subject to
6x1 + 2x2 ≥ 12high-grade ore, tons)
2x1 + 2x2 ≥ 8(medium-grade ore, tons)
4x1 + 12x2 ≥ 24 (low-grade ore, tons)
x1, x ≥ 0
a. Solve this model graphically.
b. Solve the model using Excel.