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Logan Manufacturing wants to mix two fuels, Aand B, for its trucks to minimize cost. It needs no fewer than3,000 gallons to run its trucks during the next month. it has amaximum fuel storage capacity of 4, 000 gallons. There are 2,000gallons of fuel A and 4,000 gallons of fuel B available. The mixedfuel must have the amount of fuel obtained is just equal to the sumof the amounts put it. The octane rating is the weighted average ofthe individual octanes, weighted in proportion to the respectivevolumes.
The following is known: Fuel A has an octane of 90 and costs $1.20per gallon. Fuel B has an octane of 75 and costs $0.90 pergallon.
a. Write the equations expressing this information
b. solve the problem using the Excel Solver, giving the amount ofeach fuel to be used. State any assumptions necessary to solve theproblem.
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