Consider the variation of the Wyndor Glass Co. example represented in Fig. 13.5, where the second and third functional constraints of the original problem (see Sec. 3.1) have been replaced by 9x1 2 5x2 2 216. Demonstrate that (x1, x2) (2, 6) with Z 36 is indeed optimal by showing that the objective function line 36 3x1 5x2 is tangent to this constraint boundary at

(2, 6). (Hint: Express x2 in terms of x1 on this boundary, and then differentiate this expression with respect to x1 to find the slope of the boundary.)