7. A trucking company mixes two fuels for the trucks, fuel A and fuel B. Fuel A has an octane rating of 90 and costs $1.20 per gallon. Fuel B has an octane rating of 75 and costs $0.90 per gallon. The company needs at least 3,000 gallons of the mixed fuel for operations in the next month. There are 2,000 gallons of fuel A available and 4,000 gallons of fuel B available. The mixed fuel must have an octane rating of at least 80. How many gallons of fuel A should be mixed with gallons of fuel B to minimize the fuel costs?

The octane rating of the mixed fuel is determined by a weighted mean of the two fuels.

For example, if 2 gallons of fuel A is mixed with 3 gallons of fuel B, the octane rating of the mixed fuel is (2*90 + 3*75)/(2 + 3) = 81

a) Define the decision variables.

b) Write the objective function.

c) Write the constraints in standard form.