FuelMotion is an oil company that owns two oil processing plants (in Georgia and Arizona) that produce gasoline from crude oil. Their Georgia Plant produces 2 thousand gallons of premium, 1 thousand gallons of medium, and 6 thousand gallons of regular gasoline every day it operates. Their Arizona Plant produces 3 thousand gallons of premium, 4 thousand gallons of medium and 1 thousand gallons of regular gasoline per day of operation. Chevron has placed an order for 110 thousand gallons of premium, 80 thousand gallons of medium, and 90 thousand gallons of regular gasoline and has asked for the order to be filled within 30 days. If it costs FuelMotion $10,000 per day to operate the Georgia Plant and $20,000 per day to operate the Arizona Plant, then determine how it can fill Chevron's order at minimum cost. Note that it may be necessary to produce more gas than demanded, due to the way the plants operate.
a. Formulate a linear programming model (that is, define the variables, and write down the objective function and all constraints mathematically).
b. Create a spreadsheet model for this problem and solve with Excel Solver.
c. What is the optimal solution? What is the optimal value?