A particular thermal system involves three objects of fixed shape with conduction resistances of $R_{1}=1 \mathrm{~K} / \mathrm{W}$, $R_{2}=2 \mathrm{~K} / \mathrm{W}$ and $R_{3}=4 \mathrm{~K} / \mathrm{W}$, respectively. An objective is to minimize the total thermal resistance $R_{\text {tot }}$ associated with a combination of $R_{1}, R_{2}$, and $R_{3}$. The chief engineer is willing to invest limited funds to specify an alternative material for just one of the three objects; the alternative material will have a thermal conductivity that is twice its nominal value. Which object (1, 2, or 3 ) should be fabricated of the higher thermal conductivity material to most significantly decrease $R_{\text {tot }}$ ? Hint: Consider two cases, one for which the three thermal resistances are arranged in series, and the second for which the three resistances are arranged in parallel.