Chapter 5.3, Problem 37E

The corner points for the bounded feasible region determined

by the system of linear inequalities

$\begin{array}{r}x+2y\le 10\\ 3x+y\le 15\\ x,y\ge 0\end{array}$

are $O=(0,0)$, $A=(0,5)$, $B=(4,3)$, and $C=(5,0)$.

If $P=ax+by$ and $a,b>0$, determine conditions on a and b

that will ensure that the maximum value of P occurs

(A) only at A

(B) only at B

(C) only at C

(D) at both A and B

(E) at both B and D