Optimization Problem with a ratio objective function

Question

Objective function: $$ \left\{ \begin{array}{cccc} y_1 =& 10 & + 18x_1 & + 17x_2\\ y_2 =& 100& + 40x_1& + 41x_2 \end{array} \right. \qquad \text{and} \qquad k = \frac{y_1}{y_2} $$

Constraint to:

$$ \left\{ \begin{array}{ccc} 15x_1 &+ 10x_2 &\leq 60 \\ 30x_1 &+ 40x_2 &\leq 200 \end{array} \right. $$

How do I linearise the ratio?

Do you want to maximise or minimise the ratio? – Florian Ingels Mar 30 '20 at 08:53 — Florian Ingels, Mar 30 '20 at 08:53

score 1 · Accepted Answer · answered Mar 30 '20 at 09:58

1

What you are probably looking for is this : Linear fractional programming

answered Mar 30 '20 at 09:58

Florian Ingels

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Optimization Problem with a ratio objective function

1 Answers1