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>Consider the following linear fractional program (LFP):

Consider the following linear fractional program (LFP):

$$ \begin{array}{ll} \max f\left(x_{1}, x_{2}\right)= & \frac{10 x_{1}+20 x_{2}+10}{3 x_{1}+4 x_{2}+20} \\ \text { s.t. } \quad & x_{1}+3 x_{2} \leq 50 \\ & 3 x_{1}+2 x_{2} \leq 80 \\ & x_{1}, x_{2} \geq 0 \end{array} $$

(a) Transform this problem into an equivalent linear program.

(b) Use Matlab (or other software) to solve the LP you created in part (a).

(c) Use your answer from part (a) to find a solution to the original LFP.

(d) Does your solution in part (c) satisfy the first order necessary conditions (including regularity)?

math   Statistics-And-Probability   
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