.
Really, such a problem can stump unexperienced student.
But it is not so complicated.
The solution is as follows.
From equation 8x + 2y = 18, express y = = -4x + 9 and substitute it into the expression
f(x,y) = = = = . (1)
Now your function is presented as a quadratic function of ONE argument.
You can easily find its minimum by using this very well known shortcut = " ".
In this case a = 17 and b = -72, so = = .
So, you just know the value of " x " where the function has the minimum.
By knowing , you can easily calculate = .
I leave this simple arithmetic for you to complete it on your own.
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On finding the maximum/minimum of a quadratic function see my lessons
- HOW TO complete the square to find the minimum/maximum of a quadratic function
- Briefly on finding the minimum/maximum of a quadratic function
- HOW TO complete the square to find the vertex of a parabola
- Briefly on finding the vertex of a parabola
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this textbook under the topic "Finding minimum/maximum of quadratic functions".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.