= Solution
The dual is
$$
\boxed{\text{maximize }e^Ty
\quad\text{subject to }Ay\leq e, y\geq0},
$$
which is in standard maximization form after adding nonnegative slack variables. The simplex pivots first introduce the variable with coefficient seven and then the remaining payoff column; the optimum occurs where both constraints bind:
$$
y_1+5y_2=1,
\qquad7y_1+3y_2=1.
$$
Thus $y=(1/16,3/16)$ and the dual value is $1/4$. Complementary slackness gives $x=(1/8,1/8)$. Hence $v=4$ and the normalized optimal strategies are
$$
\boxed{p=(1/2,1/2),
\qquad q=(1/4,3/4),
\qquad v=4}.
$$
Back to article page
