Commonly used for delivery of fuel products, a truck / trailer combination has five product compartments: three in the lead trailer and two in the pup trailer. The lead trailer's compartments can hold 2,700, 2,800, and 1,100 gallons of fuel respectively, while the pup compartments can hold 1,800 and 3,400 gallons of fuel respectively, for a total capacity of 11,800 gallons.

Three types of unleaded fuel (premium, mid-grade, and regular) are required at a customer's gas station. The gas station requires 2,900 gallons of premium, 4,000 gallons of mid-grade, and 4,900 gallons of regular gasoline.

Each compartment can only carry one type of fuel. The fuel supplier is under contract to meet the gas station's demand - if demand cannot be met, then the supplier will pay a penalty of $10/gallon for premium, $8/gallon for mid-grade, and $6/gallon for regular gasoline not delivered.

The maximum allowed shortage is 500 gallons for each type of fuel.

How should the company load the truck?

Part a: Should contain the mathematical formulation of the problem - decision variables, objective function and constraints.

Part b: Excel formulation worksheet and answer report.