Answer:
54880/27 = 2032 16/27
Step-by-step explanation:
You want the maximum value of 5x²y, subject to the constraints {x+y=14, x≥0, y≥0}.
Solution
Using the constraint to write an equation for y in terms of x, we have ...
5x²(14 -x) = -5x³ +70x²
The value will be maximized at a point where the derivative is zero:
-15x² +140x = 0 . . . . . derivative
-5x(3x -28) = 0 . . . . . factored
x = 0 or 28/3 . . . . . the left solution is a minimum
The value of 5x²y is maximized at x = 28/3. That maximum value is ...
5(28/3)²(42-28)/3 = 54880/27
The maximum value of 5x²y is 54880/27.
<95141404393>
