Question

4 from the vertices of the feasible region, find the maximum for the optimization function: * (1 point) f(x, y)=3x + y (0,0) (4,0) (0,5) (1.5, 5)

Explanation:

Step1: Evaluate at (0,0)

Substitute \(x = 0\) and \(y=0\) into \(f(x,y)=3x + y\).
\(f(0,0)=3\times0 + 0=0\)

Step2: Evaluate at (4,0)

Substitute \(x = 4\) and \(y = 0\) into \(f(x,y)=3x + y\).
\(f(4,0)=3\times4+0 = 12\)

Step3: Evaluate at (0,5)

Substitute \(x = 0\) and \(y = 5\) into \(f(x,y)=3x + y\).
\(f(0,5)=3\times0 + 5=5\)

Step4: Evaluate at (1.5,5)

Substitute \(x = 1.5\) and \(y = 5\) into \(f(x,y)=3x + y\).
\(f(1.5,5)=3\times1.5+5=4.5 + 5=9.5\)

Answer:

B. (4,0)