Question

2. -133.33 points Find the exact extreme values of the function :-} (x,y) - (- 6) + (y-2) + 50 subject to the following constraints: OS:5 18 OSS 13 Start by listing all nine candidates, including their z values, in the form (X,Y.2): First, list the four corner points and order your answers from smallest to largest x, then from smallest to largest y. 3) Next find the critical point. Lastly, find the four boundary points and order your answers from smallest to largest x, then from smallest to largest y. 6) 2 B) Finally, find the extreme values at (x,y) - ( Note that since this is a closed and bounded feasibility region, we are guaranteed both an absolute maximum and absolute minimum value oft bola formatting help

Answer 1

summary:- First we partially differentiate f(x,y) with respect to x and y respectively. Then put this equal to 0 to find out value of x and y.

Here this (x,y) is critical point. Now check whether at critical point function is maximum or minimum by formula.

We see at critical point function attains its minimuk value which is 50. To find maximum value we put (x,y) = (0,0) , then we attain maximum value is 90.

za finy) = (x-61² + 14-23² + so at 2 2 1x-6) = of 20 - 214-670 ) x = 6 ay = 27.a) - 914-2)=0 >> y=2 Critical point is lay)= 16,2). Now fun fun - [tay J² = 2.2 -0 = 450 So at (612) : finyl is minimum. fin (6,2)= 16-63² + 12-28 + 50 = otot 5o= 50 frin (16, 2) = 5o. Squave Since all terms are positive & in finy) so find maximum value off we feut wy) = 10,0) f 10,0)= (0-62+ (0-28+ 50 = (-62+ (-2)² + 5o = 36+ 4+so tman (0,0) = 90 Critical point (% 4, 2) = (6, 2,50). fimin = 50 at 1my)= 16,2). fmox = 90 at (ny) = 10,0).