A System Consists Of Two Power Plants That Must Deliver

A system consists of two power plants that must deliver loads over a transmission network. The costs of generating power at plants 1 and 2 are given by
F1 = 2p1 + 2
F2 = 10p2
Where p1 and p2 = power produced by each plant. The losses of power due to transmission L are given by
L1 = 0.2p1 + 0.1p2
L2 = 0.2p1 + 0.5p2
The total demand for power is 30 and p1 must not exceed 42. Determine the power generation needed to meet demands while minimizing cost using an optimization routine such as those found in, for example, Excel, MATLAB software, and IMSL.

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