Question: Question 1: GeoTherm Mining Company owns two mines each can produce three different 2racies of coal: high, medium, and low. During each hour of operation, mine 1 produces 6 toms of high-grade coal, 2 tons of medium-grade coal, and 4 tons of low-grade coal. Mine 2 produces 2 tons of high-grade coal, 2 tons of medium-grade coal, and 8 tons of low-grade coal per hour of operation. It costs $2000 per hour to operate mine 1 and $1600 to operate mine 2. To fulfill its contractual obligations to a local power-plant GeoTherm has to supply at least 12 tons of high-trade coal. S tons of medium-grade coal, and 24 tons of low-grade coal per day.

Answer the following:

a. Define appropriate variables.

b. Develop the appropriate LP model. Solve using Graphical Method (only).

c. Find the minimum possible cost.

d. Calculate slacks (surplus) for each constraint

e. State the binding constraints.

f. Manually calculate the dual prices for each constraint and interpret non-zero dual prices.