Following your recommended strategy. Chemicals, Inc. wanted to develop an improved aviation fuel to be used by commercial jets at minimal cost. The fuel is a mixture of two fuels (Avgas A and Avgas B). There are 4,000 gallons of Avgas A and 8,000 gallons of Avgas B available. It needs no fewer than 6,000 gallons to fuel a jet to its farthest destination which has a maximum fuel storage capacity of 8,000 gallons. The mixed fuel must have an octane rating of no less than 80. The octane rating is the weighted average of the individual octanes, weighted in proportion to the respective volumes. During mixture, the amount of Avgas obtained equals to the sum of the amounts put in. Avgas A has an octane of 90 and costs $2.40 per gallon. Avgas B has an octane of 75 and costs $1.80 per gallon. In presenting your findings to Chemicals, Inc., they would like to see:
a. The equations expressing this information. b. Your solutions using the graphical method. c. The optimal equation that would meet their objective.