Question 1) Find the exact extreme values of the function

z= f (x,y) = 39x+10y+70

subject to the following constraints:

y greater than or equal to(>) 0

y less than or equal to (<) 36-x^2

Complete the following:

fminat (x,y) = (,)

fmaxat (x,y) = (,)

Note that since this is a closed and bounded feasibility region, we are guaranteed both an absolute maximum and absolute minimum value of the function on the region.

Question 2) Find the exact extreme values of the function

z=f (x,y) = 3x^2-2xy+4y^2-6x-20y+9

subject to the following constraints:

0 is less than or equal to (<) x less than or equal (<) to 5

0 is less than or equal to (<) y less than or equal (<) to 6

Start by listing all nine candidates, including their z values, in the form (x,y,z):

First, list the four corner points and order your answers from smallest to largestx, then from smallest to largesty.

1) (0,0 ,9)

2) (, , ,)

3) (,, ,)

4) (,,,)

Next find the critical point.

5) (,,,)

Lastly, find the four boundary points and order your answers from smallest to largestx, then from smallest to largesty.

6) (,,,)

7) (,,,)

8) (,,,)

9) (,, ,)

Finally, find the extreme values:

fminat (x,y) = (,)

fmaxat (x,y) = (,)

Note that since this is a closed and bounded feasibility region, we are guaranteed both an absolute maximum and absolute minimum value of the function on the region.