Optimizing a Circuit

The DC circuit above consists of two voltage sources V1V_1 and V2V_2 with internal resistances R1=1ΩR_1 = 1 \Omega and R2=2ΩR_2 = 2 \Omega respectively. There is a load RL=3ΩR_L = 3 \Omega connected in parallel with the sources.

V1V_1 and V2V_2 are variable quantities.

Let P1P_1, P2P_2, and PLP_L be the amounts of power in watts dissipated by R1R_1, R2R_2, and RLR_L respectively.

Given that PL=10P_L = 10 watts, determine the minimum possible value of P1+P2+PLP_1 + P_2 + P_L to 1 decimal place.

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