# Maximization (mathematical problems)

Maximize for $$P = 5x - 2y$$:

\begin{align} & y \le 5 \\ & x \le 4 \\ & y \ge -x \end{align}

Maximize for $$P = 3x + 5y$$:

\begin{align} & 3x + 2y \le 12 \\ & x + y \le 5 \\ & x \ge 0 \\ & y \ge 0 \end{align}

Maximize for $$P = 3x + 2y$$:

\begin{align} & 2 \le x \le 6 \\ & 1 \le y \le 5 \\ & x + y \le 8 \end{align}

Maximize for $$P = 2x + y$$:

\begin{align} & 3x + y \le 7 \\ & x + 2y \le 9 \\ & x \ge 0 \\ & y \ge 0 \end{align}

Maximize for $$P = x + 3y$$:

\begin{align} & x + y \le 5 \\ & x + 2y \le 8 \\ & x \ge 0 \\ & y \ge 0 \end{align}

Maximize for $$P = 2x + y$$:

\begin{align} & 3x + y \le 7 \\ & x + 2y \le 9 \\ & x \ge 0 \\ & y \ge 0 \end{align}

Maximize for $$P = 4x + 3y$$:

\begin{align} & 6 \le x + y \le 13 \\ & x \ge 3 \\ & y \ge 1 \end{align}

Maximize for $$P = 2x + y$$:

\begin{align} & 3x + y \le 7 \\ & x + 2y \le 9 \\ & x \ge 0 \\ & y \ge 0 \end{align}

Maximize for $$P = 3x + 2y$$:

\begin{align} & x \ge 0 \\ & y \ge 0 \\ & x + 2y \le 4 \\ & x - y \le 1 \end{align}

Maximize for $$P = 4x + 2y$$:

\begin{align} & x \ge 0 \\ & y \ge 0 \\ & x + 2y \ge 4 \\ & 3x + y \ge 7 \\ & -x + 2y \le 7 \end{align}