A satellite requires a battery with an open-circuit voltage (v_{mathrm{OC}}=) (36 mathrm{~V}) and a Thvenin resistance (R_{mathrm{T}}

A satellite requires a battery with an open-circuit voltage \(v_{\mathrm{OC}}=\) \(36 \mathrm{~V}\) and a Thévenin resistance \(R_{\mathrm{T}} \leq 102\). The battery is to be constructed using series and parallel combinations of one of two types of cells. The first type has \(v_{\mathrm{OC}}=9 \mathrm{~V}, R_{\mathrm{T}}=4 \Omega\), and a weight of \(30 \mathrm{~g}\). The second type has \(v_{\mathrm{OC}}=4 \mathrm{~V}, R_{\mathrm{T}}=2 \Omega\), and a weight of \(18 \mathrm{~g}\). Design a minimum weight battery that meets the open-circuit voltage and Thévenin resistance requirements.