The figure below shows a direct current electrical network. A mathematical programming model can be used to find the current flows I₁, I₂ and I₃. The current flows are the variables of the model.

a. The model requires the single constraint:

.

Explain the purpose of this constraint.

b. Write the nonlinear objective function that when minimized will determine the values of the currents.

c. When the model is solved with a procedure such as the Solver in Excel, is one assured of global optimum? Justify your conclusions based on the constraint of part a and the objective of part b.