In the electrical circuit of Figure 11. It = current (in amperes) flowing through resistor...

In the electrical circuit of Figure 11. It = current (in amperes) flowing through resistor t, Vt, = voltage drop (in volts) across resistor t, and R, = resistance (in ohms) of resistor t. Kirchoff’s Voltage and Current Laws imply that V1 = V2 = V3, and I1 + I2 + I3 = I4. The power dissipated by the current flowing through resistor t is I2tRt. Ohm’s Law implies that Vt = ItRt. The two pans of this problem should be solved independently.

a Suppose you are told that I1, = 4, I2 = 6, I3 = 8, and I4 = 18 are required. Also, the voltage drop across each resistor must be between 2 and 10 volts. Choose the Rt’s to minimize the total dissipated power. Formulate an LP whose solution will solve your problem.

b Suppose you are told that V1 = 6, V2 = 6, V3 = 6, and V4 = 4 are required. Also, the current flowing through each resistor must be between 2 and 6 amperes. Choose the Rt’s to minimize the total dissipated power. Formulate an LP whose solution will solve your problem. (Hint: Let  be your decision variables.)