Using Lagrange multipliers, we have the Lagrangian

with partial derivatives (set equal to 0)




Substituting the first three equations into the fourth allows us to solve for

:

For each possible value of

, we get two corresponding critical points at

.
At these points, respectively, we get a maximum value of

and a minimum value of

.
X=58 the exterior angle is “D” 60degrees
14/15-5/12 = 31/60
31/60 = 0.5166...
He can travel 500 miles if he spends $200.
Hope this helps :)