[See Solution] (a) Solve the problem of minimizing x_1^2+(x_2-1)^2 subject to x_1≥ e^x_2 (b) Solve the problem of maximizing f(x) subject to g(x)≤ 0, where
Question: (a) Solve the problem of minimizing \(x_{1}^{2}+{{\left( {{x}_{2}}-1 \right)}^{2}}\) subject to \({{x}_{1}}\ge {{e}^{{{x}_{2}}}}\)
(b) Solve the problem of maximizing \(f\left( x \right)\) subject to \(g\left( x \right)\le 0\), where \(f\left( x \right)=x\) and
\[g\left( x \right)=\left\{ \begin{aligned} & {{x}^{4}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\le 0 \\ & 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\in \left[ 0,1 \right] \\ & {{\left( x-1 \right)}^{4}}\,\,\,\,x\ge 1 \\ \end{aligned} \right.\]
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(Step-by-Step) Given the utility function U=x_1^alpha x_2^beta ,
![[See Steps] Solve the problems of: Maximizing](/images/solutions/MC-solution-library-34270.jpg "[See Steps] Solve the problems of: Maximizing U=(x_1x_2)^3+x_1x_2,")
[See Steps] Solve the problems of: Maximizing U=(x_1x_2)^3+x_1x_2,
![[See Solution] Given the utility function U=x_1^alpha](/images/solutions/MC-solution-library-34271.jpg "[See Solution] Given the utility function U=x_1^alpha x_2^beta , where")
[See Solution] Given the utility function U=x_1^alpha x_2^beta , where
(Solution Library) Prove that a diminishing marginal rate of substitution
[Solved] maximizing U=(x_1x_2)^3+x_1x_2, subject to p_1x_1+p_2x_2=y,
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