Given: Q = 20K0.3 L0.7, C* = $1,000, r = $30 and w = $10. Determine the amount of labor and capital that maximizes output and determine the optimal amount of output. Calculate and interpret the Lagrangian multiplier.
"Q=20K^{0.3}L^{0.7}+\\lambda (1000-30K-10L)"
"\\frac{\\delta Q}{\\delta K}=6(\\frac{L}{K})^{0.7}-30 \\lambda"
"\\frac {\\delta Q}{\\delta L}=14(\\frac{K}{L})^{0.3}-10\\lambda"
"L=7K"
"K=10"
"L=70"
"\\lambda=0.78"
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