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Problem*: Ernesto is about to take a history test consisting of matching questions worth 10 points each and essay questions worth 25 points each. He is required to do at least 3 matching questions, but there are only 12 matching questions. Similarily, he must do at least 4 essays, but there are only 15 essay questions. Ernesto's teacher will grade at most a total of 20 questions. How many of each type should he answer to maximum his score? What is this maximum possible score?
Solution
The Problem asks how many questions of each type so we let these be our variables:
Let x=number of matching questions and let y=number of essay questions.
Reading we see that we have the 4 constraints: 3 ≤ x ≤12 and4 ≤ y ≤15.
From the problem we get our 5th constraint: x+y≤20
Finally, our objective function which we need to maximize is points: P=10x+25y.
Let's solve this problem using GeoGebra! Watch the mathcast, study the interactivity below and then do it yourself.
Example 1
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