Minimer C(K,L)=4K+LC(K,L) = 4K + LC(K,L)=4K+L gitt produksjonskravet K1/2L1/2=10K^{1/2}L^{1/2} = 10K1/2L1/2=10.
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L=4K+L−λ(K1/2L1/2−10)\mathcal{L} = 4K + L - \lambda(K^{1/2}L^{1/2} - 10)L=4K+L−λ(K1/2L1/2−10). 4=λL1/22K1/2\displaystyle 4 = \frac{\lambda L^{1/2}}{2K^{1/2}}4=2K1/2λL1/2 og 1=λK1/22L1/2\displaystyle 1 = \frac{\lambda K^{1/2}}{2L^{1/2}}1=2L1/2λK1/2. Divisjon: 4=LK⇒L=4K\displaystyle 4 = \frac{L}{K} \Rightarrow L = 4K4=KL⇒L=4K. Inn: K1/2(4K)1/2=2K=10⇒K=5K^{1/2}(4K)^{1/2} = 2K = 10 \Rightarrow K = 5K1/2(4K)1/2=2K=10⇒K=5, L=20L = 20L=20. Min C=40C = 40C=40.
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