In this exercise we have to use the knowledge of function to write the minimum production cost, so we have to:
[tex]K=13.975[/tex]
Thus writing the function that corresponds to this will be:
[tex]MPK = Q'(K) = 50L^{0.5}/K^{0.5} = 25\\MPL = Q'(L) = 50K^{0.5}/L^{0.5} = 100[/tex]
Now calculating the minimum production cost we have:
[tex]MPK/r = MPL/w\\MPK/40 = 100/50\\MPK =80\\MPK = 50L^{0.5}/K^{0.5} = 80\\K=(1.118/80)= 13.975[/tex]
See more about functions at brainly.com/question/14674614
