A particular thermal system involves three objects of fixed shape with conduction resistances of R1 = 1 K/W, R2 = 2 K/W and R3 = 4 K/W, respectively. An objec- tive is to minimize the total thermal resistance Rtot asso- ciated with a combination of R1, R2, and R3. 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 conductiv- ity that is twice its nominal value. Which object (1, 2, or 3) should be fabricated of the higher thermal con- ductivity material to most significantly decrease Rtot? Hint: Consider two cases, one for which the three ther- mal resistances are arranged in series, and the second for which the three resistances are arranged in parallel.