Expert: Robi Bhattacharjee - 11/2/2008

Question
Chapter 7- Linear Programming

Write the constraints as linear inequalities and identify the variables.

The manufacturing process requires that oil refineries manufacture at least 2 gallons of gasoline for every gallon of fuel oil. To meet the winter demand for fuel oil, at least 3 million gallons a day must be produced. The demand for gasoline is no more than 12 million gallons per day. It takes .25 hour to ship each million gallons of gasoline and 1 hour to ship each million gallons of fuel oil out of the warehouse. No more than 6.6 hours are available for shipping. If the refinery sells gasoline for $1.25 per gallon and fuel oil for $1 per gallon, how much of each should be produced to maximize revenue. Find the maximum revenue.

I understand that at least means greater than or equal to and no more than means less than or equal to. But I am not sure how to put this word problem in inequalities form.

I am thinking that $1.25 and $1 would be 1.25x + 1y less than or greater than or equal to the number of gallons that should be produced. Am I right?

Answer
Hi Jeffery,

When it says not more than, what it means is less than or equal to. Conversely, when it says not less than, it means greater than or equal to. Now for the inequalities.

Let x be the amount of of gasoline and y be the amount of fuel oil.

So y > equal to 2x since there must be at least 2 gallons of gasoline for each crude oil.

Basically, key is to be able to transform sentences into equations. Now this is a skill that can only be developed by practice. So to solve these kinds of questions, simply transform the sentences into equations as I did and then you will be okay.


I hope this helped.
Robi