Decide whether the given point is a corner point for the constraints

\[\left\{\begin{array}{l}x \geq 0 \\y \geq 0 \\2 x+3 y \geq 120 \\2 x+y \geq 80 \end{array}ight.\]

a. \((0,0)\)

b. \((0,80)\)

c. \((80,0)\)

d. \((60,0)\)

e. \((30,20)\)

f. \((20,30)\)