word question

Question

A refinery produces both gasoline and fuel oil, and sells gasoline for $1.00 per gallon and fuel oil for .90 cents per gallon.  The refinery can produce at most 600,000 gallons a day, but must produce at least 2 gallons of fuel oil every gallon of gasoline.  At least 150,000 gallons of fuel oil must be produced each day to meet demand.  How much of each type should be produced daily to maximize daily profits?  Show me how.

Answer 1

Answer: 400,000 gallons of fuel oil and 200,000 gallons of gasoline

 

Your first constraint of importance is that you must produce a 2 to 1 ration of fuel oil to gasoline.  So for every three gallons you must have 2 fuel oil and one gasoline.  Dividing 600,000 by three gives you 200,000.  So 200,000 times 2 gives you 400,000 fuel oil and 200,000 times 1 gives you 200,000 gasoline for a total of 600,000.

 

Your second constraint is that at least 150,000 gallons of fuel oil must be produced.  Since 400,000 is greater than 150,000 you easily meet this constraint.

 

Finally, you will not produce more than 400,000 gallons of fuel oil since the gasoline is more profitable to produce.  Indeed if you did not have the first constraint you would be producing more than 200,000 gallons of gasoline.