 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2015/prelims/mathematics-iv/5/b/i/solution

There are two primal inequalities, so there are two nonnegative dual variables. The five primal variables yield five dual inequalities:

minimise 2 y_{1} + y_{2}, y_{1} + y_{2} \geq 1, - y_{1} + y_{2} \geq - 1, - y_{1} + 3 y_{2} \geq - 5, 3 y_{1} + 4 y_{2} \geq 12, 3 y_{1} + y_{2} \geq 6, y_{1}, y_{2} \geq 0.

Each coefficient column of the primal linear program becomes one row of this dual linear program.

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