Question 199721
Wish I had a nice tool to do this, but I don't. In this case, I used trial and error.

Let's look at the answers first. 
a) can't be correct since a max of -96 and a min of 0 doesn't make sense.

Let's look at c) next. Those numbers look good, so let's see if we can work backwards to values for x and y. Then we can use the givne constraints to see if they are satisfied.
First, look at P, You can see that P grows as x gets larger and shrinks as y get larger. So, pick the largest value allowed for x and the the smallest one allowed for y. That means pick x=5 and y =0. If we use (5,0), then P=50. So far, so good. Now check the other constraints. Is 4x + 5y <= 30, and 4x + 3y <= 20 satisfied at (5,0)? Yes. So (5,0) still looks OK.
What about a minimum?
In that case, use the smallest x and the largest y. So (0,8) yields the minimum for P. Test the contraints  4x + 5y <= 30, and 4x + 3y <= 20 satisfied at (0,8)? No. So let's pin x at 0 and see what value for y works for the constraints. You can see the first one says y<=6 and the second says y<=20/3. So y=6 fits for both. Try point (0,6). What is P then? P = 10*0 - 16*6 = -96

c) is the answer

the values in b) are valid, but the max is incorrect