Answer:
A. at (8,7) the maximum value is 98
Step-by-step explanation:
First draw the region, that is bounded by all inequalities. This is the triangle with vertices (6,1), (2,5) and (8,7).
Now you can see where the line f(x,y)=7x+6y intersect this region. The maximum value will be at endpoints of this region:
- at (6,1), f(6,1)=7·6+6·1=42+6=48;
- at (2,5), f(2,5)=7·2+6·5=14+30=44;
- at (8,7), f(8,7)=7·8+6·7=56+42=98.
Thus, the maximum value of the function is 98 at the point (8,7).
