Final answer:
To evaluate the function f(x, y) at the point (3,1), we substitute the values into the equation and simplify to find that f(3,1) equals 196.
Step-by-step explanation:
The question is asking to evaluate the function f(x, y)=50x+80y-3x²-4y²-xy at the point (3,1). To do this, we substitute x with 3 and y with 1:
- f(3, 1) = 50(3) + 80(1) - 3(3)² - 4(1)² - (3)(1)
- f(3, 1) = 150 + 80 - 27 - 4 - 3
- f(3, 1) = 230 - 27 - 4 - 3
- f(3, 1) = 196
Therefore, f(3,1) evaluates to 196.