Answer in Microeconomics for isaac mensah #179255

Given utility maximization problem U= Q1Q2 subject to 10Q1 +2Q2=240 a. Derive the Lagrange function b. Derive the first order conditions c. Use Cramer’s rule to find the critical values of Q1, Q2 and �

i.) Deriving the Lagrange function:

“Z = Q1Q2+ u03bb(240-10Q1-2Q2)”

ii.) first-order conditions:

“ZQ1 = Q2u2212 u03bb10 = 0\nnn ZQ2 = Q1u2212 u03bb 2 = 0 \nnnZu03bb = 240 u2212 10Q1 u22122 Q2 =0.”

“Zlambda=240-10Q1-2Q2=0”

“ZQ1=Q2- lambda10=0”

“ZQ2=Q1-lambda2=0”

iii.) “begin{bmatrix}n 0 & -10 & -2 \n -10 & 0 &1 \n-2 & 1 & 0nend{bmatrix}” “begin{bmatrix}n lambda \n Q1 \ Q2nend{bmatrix}” = “begin{bmatrix}n -240 \n 0 \ 0nend{bmatrix}”

Q1^M“=frac{240}{2[-10]}= -12”

Q2^M“=frac{240}{2[-2]}=-60”

“lambda=frac{240}{2[-10.-2]}=6”