 Home

Codex Wiki

List of universities

University of Oxford

Course of the University of Oxford

Undergraduate course of the University of Oxford

Mathematics and statistics course of the University of Oxford

Year 2 of the mathematics and statistics course of the University of Oxford

Probability, statistics and options II course of the University of Oxford

Past exam of the Probability, statistics and options II course of the University of Oxford

2007

Introduce nonnegative <slack variables> $s_1,s_2$ and use a <simplex tableau> with the last row representing $z-c^{\mathsf T}x=0$. The starting tableau is
$$
\begin{array}{c|rrrrr|r}
&x_1&x_2&x_3&s_1&s_2&\text{RHS}\\\hline
s_1&2&3&5&1&0&33\\
s_2&1&2&3&0&1&18\\\hline
z&-3&-4&-8&0&0&0
\end{array}
$$
Enter $x_3$ and let $s_2$ leave. Dividing the second row by three and eliminating its column gives
$$
\begin{array}{c|rrrrr|r}
&x_1&x_2&x_3&s_1&s_2&\text{RHS}\\\hline
s_1&1/3&-1/3&0&1&-5/3&3\\
x_3&1/3&2/3&1&0&1/3&6\\\hline
z&-1/3&4/3&0&0&8/3&48
\end{array}.
$$
Enter $x_1$ and let $s_1$ leave. The next <simplex tableau> is
$$
\begin{array}{c|rrrrr|r}
&x_1&x_2&x_3&s_1&s_2&\text{RHS}\\\hline
x_1&1&-1&0&3&-5&9\\
x_3&0&1&1&-1&2&3\\\hline
z&0&1&0&1&1&51
\end{array}.
$$
Thus
$$
\boxed{(x_1,x_2,x_3)=(9,0,3),\qquad z_{\max}=51.}
$$
The pivot choices and the optimality certificate are justified in the following parts.

Solution

Past exam of the Probability, statistics and options II course of the University of Oxford / 2007 / T / 2 / b / Solution

Past exam of the Probability, statistics and options II course of the University of Oxford / 2007 / T / 2 / b / Solution

 Ancestors (13)

 Discussion (0) New discussion

 Articles by others on the same topic (0)

Past exam of the Probability, statistics and options II course of the University of Oxford / 2007 / T / 2 / b / Solution

 Ancestors (13)

 Discussion (0)  Subscribe (1) New discussion

 Articles by others on the same topic (0)

 Discussion (0) New discussion