Problem 13 Solution

Let U=happiness.

U=w²*c.

3*w + 2*c = 100.

c=(100-3w)/2.

U=w²*(100-3w)/2.

dU/dw=2w*(100-3w)/2 + w²*-3/2=0.

Solving for w yields w=200/9.

With wine costing $3 a glass this will cost 3*200/9=$66.67, leaving $33.33 for cigars, for which he can buy 16.67.

Michael Shackleford, A.S.A.