Chapter 10.FOM, Problem 16P

Feasible Region All parts of this problem refer to the following feasible region and objective function.

$\{\begin{array}{l}x\ge 0\\ x\ge y\\ x+2y\ge 12\\ x+y\le 10\end{array}$

$P=x+4y$

(a) Graph the feasible region.

(b) On your graph from part (a), sketch the graphs of the linear equations obtained by setting $P$ equal to $40$, $36$, $32$, and $28$.

(c) If you continue to decrease the value of $P$, at which vertex of the feasible region will these lines first touch the feasible region?

(d) Verify that the maximum value of $P$ on the feasible region occurs at the vertex you chose in part (c).