calculus tutor online Online Tutorial: Lagrange Multipliers

Given a generalized utility function f = Phi * x^X * y^Y * z^Z * a^A * b^B and the constraint

X1x + Y1y + Z1z + A1a + B1b = Q

Find the values x, y, z, a, b to maximize utility.

Where Phi is a constant, lowercase variable is the amount of that item, uppercase variable is a given exponent in the utility function, uppercase variable sub 1 is the cost per unit of that item.

This solution uses lagrange multipliers.

We also solve the same problem algebraically using the gradient operator in another video. Compared to solving algebraically, you can see how powerful lagrange multiplier concept is.



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