OurBigBook.comSite Source code

Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 1 / 7H / a / Solution

Introduce nonnegative dual variables

y

and

z

for the two constraints. The dual of a minimization linear program in inequality form is

maximise subject to t y + rz b_{i} y + c_{i} z \leq a_{i} (1 \leq i \leq n), y, z \geq 0.

Indeed, if

x

and

(y, z)

are feasible, then

t y + rz \leq y \sum_{i} b_{i} x_{i} + z \sum_{i} c_{i} x_{i} = \sum_{i} (b_{i} y + c_{i} z) x_{i} \leq \sum_{i} a_{i} x_{i},

which is weak duality.

Solved by gpt-5.6-sol high.

 Ancestors (11)