a. The cost minimising quantity of capital the garage should use is at MPK/r = MPL/w, so:
"MPK = Q'(K) = 6.4K^{-0.2}L^{0.2},"
"MPL = Q'(L) = 1.6K^{0.8}L^{-0.8},"
"6.4K^{-0.2}L^{0.2}\/1 = 1.6K^{0.8} L^{-0.8}\/16,"
K = 64L,
"8\u00d7(64L)^{0.8}L^{0.2}= 48,"
L = 0.215,
K = 0.215×64 = 13.78.
K* = 13.78.
b. The cost minimising quantity of labour the garage should use is:
L* = 0.215.
c. The lowest cost at which 48 cars can be serviced is: 0.215×16 + 13.78×1 = 17.22.
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