Logan Manufacturing wants to mix two fuels, A and B , for its trucks to minimize cost. It needs no fewer than 3,000 gallons to run its trucks during the next month. It has a maximum fuel storage capacity of 4,000 gallons. There are 2,000 gallons of fuel A and 4,000 gallons of fuel B available. The mixed fuel must have an octane rating of no less than 80. When fuels are mixed, the amount of fuel obtained is just equal to the sum of the amounts put in. The octane rating is the weighted average of the individual octanes, weighted in proportion to the respective volumes.
The following is known: Fuel A has an octane of 90 and costs $1.20 per gallon. Fuel B has an octane of 75 and costs $0.90 per gallon.
a. Write the equations expressing this information.
b. Solve the problem using the Excel Solver, giving the amount of each fuel to be used. State any assumptions necessary to solve the problem.