Both x and y are positive real numbers, and the point (x,y) lies on or above both of the lines having equations 2x+5y=10 and 3x+4y=12. What is the least possible value of 8x+13y?
I graphed the equations \(2x+5y>10\) and \(3x+4y>12\), then just found the optimal point.
To find the optimal point, I graphed \(8x+13y=k\) and then found the point where that line first touched the region.
It was at (2.857, 0.857) to the nearest thousandth.
Then I did the math and got 34.
You are very welcome!