w=9
r=4
q=1200
q=100L21K21
Derive MPL and MPK
MPL = ∂L∂Q = 50L-0.5K0.5
MPK = ∂K∂Q = 50L0.5K-0.5
MPKMPL = rw
w = 9
r = 4
50L-0.5K0.5 ÷ 50L0.5K-0.5 = 49
50L0.5K−0.550L−0.5K0.5=49
LK=49
K=49L
Substitute this value in the production function
q=100(49L)0.5L0.5
1200=100(413L)0.5
L0.5=(100)(3.25)0.51200
L=((100)(3.250.51200)2
=325001440000=44.31
K=49L
K=49×44.31=99.69
TC= wL+rK
720=9L+4K
But L=49K
720=9L+49L
720=445L
L=45(720×4)=64
K=49×64=144
Total Output=144+64= 208
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