7 In an electrical network, the power loss incurred when a current of I amperes flows through a resistance of R ohms is I2R watts. In Figure 48, 710 amperes of current must be sent from node 1 to node 4. The current flowing through each node must satisfy conservation of flow. For example, for node 1, 710 flow through 1-ohm resistor flow through 4-ohm resistor. Remarkably, nature determines the current flow through each resistor by minimizing the total power loss in the network.

a Formulate a QPP whose solution will yield the current flowing through each resistor.

b Use LINGO to determine the current flowing through each resistor.

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710 4 2 12 3 710