59 In the electrical circuit of Figure 11, It = current (in amperes) flowing through resistor t, Vt = voltage drop (in volts) across resistor t, and Rt = 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 It 2 Rt. Ohm’s Law implies that Vt = ItRt. The two parts 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 1/R_T (t = 1, 2, 3, 4) be your decision variables.)