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# hw04_2008 - WELL AS THE CHOICE VARIABLES SHOW YOUR WORK(5 2...

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UNC-Wilmington ECN 321 Department of Economics and Finance Dr. Chris Dumas Homework 4 (Due Thursday, October 16) Solve the following nonlinear optimization problems without constraints . Be sure to read the handout on the class website that covers nonlinear optimization problems without constraints! (1) max U = 10 + 3ln(X) + X -1 X subject to: no constraints (2) max U = 20 + 100X – 2X 2 X subject to: no constraints (3) max U = 40 + 60X 1 - (1/4)X 1 2 + 100X 2 - (1/3)X 2 2 X 1 , X 2 subject to: no constraints (4) max U = 300X 1 + 6000X 2 - (1/3)X 1 2 - 3X 2 2 – (1/4)X 1 X 2 X 1 , X 2 subject to: no constraints Solve the following non-linear optimization problems with constraints . USE LAGRANGE'S METHOD. SOLVE FOR THE OPTIMAL VALUES OF THE LAGRANGIAN MULTIPLIERS AS
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Unformatted text preview: WELL AS THE CHOICE VARIABLES. SHOW YOUR WORK. (5) 2 X X 2 X 50 2400 U max-+ = subject to: \$2X ≤ \$300 (6) ) Z ln( 10 20 U max Z ⋅ + = subject to: Z ≤ 30 (Recall that there is an understood “one” to the left of Z.) (7) Y 200 X 300 X ) 2 / 1 ( 30 Y ) 3 / 1 ( U 2 2 Y , X max + +-+-= subject to: \$2X + \$1Y ≤ \$100 (8) 4 / 1 3 / 2 Y , X Y X 20 U max ⋅ ⋅ = subject to: (2hrs)X + (3hrs)Y ≤ 36hrs (9) 5 / 1 2 / 1 S , R S R 3 U max ⋅ ⋅ = subject to: \$8R + \$3S ≤ \$4000 (10) In words (not symbols or math), what is the definition of the Lagrange Multiplier?...
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