Logan Manufacturing wants to mix two fuels. A and B for its trucks to minimize cost. It needs no fewer than 3,500 gallons to run its trucks during the next month. It has a maximum fuel storage capacity of 4,000 gallons. Thre are 2,300 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 proportation to the respective volumes. The following is known: Fuel A has an octane of 97 and costs $1.50 per gallon. Fuel B has an octane of 71 and costs $1.70 per gallon. A. Write the equations expressing this information.
Logan Manufacturing wants to mix two fuels. A and B for its trucks to minimize cost. It needs no fewer than 3,500 gallons to run its trucks during the next month. It has a maximum fuel storage capacity of 4,000 gallons. Thre are 2,300 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 proportation to the respective volumes.
The following is known: Fuel A has an octane of 97 and costs $1.50 per gallon. Fuel B has an octane of 71 and costs $1.70 per gallon.
A. Write the equations expressing this information.
| Z = | A + | B |
s.t
| Fuel Demand | A + | B > | |||
| Storage | A + | B < | |||
| Fuel A available | A + | B < | |||
| Fuel B available | A + | B < | |||
| Blend | A + | B > |
B. Solve the problem using the Excel Solver, giving the amount of each fuel to be used.
| Decision for A | |
| Decision for B | |
| Total Cost |
| Resources Used | |
| Demand | |
| Storage | |
| Fuel A | |
| Fuel B | |
| Blend |
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