Question

Verify maximum Q=f(L,K) subject c=wl + rk

Answer 1

$Q=f(L,K)$

Q =quantity of output produced.

K= is capital input.

L= is labor input.

F= is a functional form relating the inputs to output. 

$c=wl + rk$

c=wage×labour +interest×capital

rearranging

$K=(\frac{1}{r})c-(\frac{W}{r})L$

$MRTS_{KL}=\frac{W}{r}$