Chapter 16, Problem 24P

A system consist softwopower plants that must deliver loads over a transmission network. The costs of generating power at plants 1 and 2 are given by

$\begin{array}{l}{F}_1=2p_1+2\\ F_2=10p_2\end{array}$

where $p_1$ and $p_2=$ power produced by each plant. The losses of power due to transmission L are given by

$\begin{array}{l}{L}_1=0.2p_1+0.1p_2\\ L_2=0.2p_1+0.5p_2\end{array}$

The total demand for power is 30 and $p_1$ must not exceed 42. Determine the power generation needed to meet demands while minimizing costusing an optimization routine such as those found in, for example, Excel, MATLAB, or Mathcad software.