LGT Sheet

Question 1

(i)

Maximise $3x+4y$. Subject to:

$$\begin{array}{rl}x+y& \le 7\\ x-4y& \ge -13\\ x& \le y+4\end{array}$$

(ii)

Maximise $x+5y$, $C=x+5y\Rightarrow -x-5y+C=0$. Subject to:

$$\begin{array}{rl}y-x& \le 5\\ 3y-2x& \ge 0\\ 2y+x& \le 16\end{array}$$

Add slack variables:

$$\begin{array}{rl}y-x+s_0& =5\\ -3y+2x+s_1& =0\\ 2y+x+s_2& =16\end{array}$$

Solve:

$$\left[\begin{array}{ccccccc}x& y& s_0& s_1& s_2& C& \\ -1& 1& 1& 0& 0& 0& 5\\ 2& -3& 0& 1& 0& 0& 0\\ 1& 2& 0& 0& 1& 0& 16\\ -1& -5& 0& 0& 0& 1& 0\end{array}\right]$$