Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 4 / 18H / d / Solution

The dual iswhich 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: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

Solved by gpt-5.6-sol high.