Question

A firm wants to minimize cost when Q=160=2√KL ;r=4 k=2
find K and L

Answer 1

$2 \sqrt{KL}=160 \\ L = 2l+4K-λ[\sqrt{KL} -80] \\ \frac{∂L}{∂l} = 2 - \frac{λ}{2} \sqrt{\frac{K}{l}} =0 \\ λ = 4 \sqrt{\frac{l}{K}} \\ \frac{∂L}{∂K} = 4 -\frac{λ}{2} \sqrt{\frac{K}{l}} \\ l = 2K \\ 2 \sqrt{2} K =160 \\ K=56.58 \\ L=113.15$