Consider the variation of the Wyndor Glass Co. problem represented in Fig. 13.6, where the original objective function (see Sec. 3.1) has been replaced by Z 126x1  9x1 2 182x2 

13x2 2

. Demonstrate that (x1, x2) (

8 3

, 5) with Z 857 is indeed optimal by showing that the ellipse 857 126x1  9x1 2

182x2  13x2 2 is tangent to the constraint boundary 3x1 2x2 18 at (

8 3

, 5). (Hint: Solve for x2 in terms of x1 for the ellipse, and then differentiate this expression with respect to x1 to find the slope of the ellipse.)