Question 199721: Can someone please help me with this problem:
Find the value(s) of the function, subject to the system of inequalities.
Find the maximum and minimum of P = 10x - 16y subject to:
0 < X < 5, 0 < Y < 8, 4x + 5y < 30, and 4x + 3y < 20
***ALL OF THE < SIGNS HAVE A LINE UNDER THEM***
a. -96, 0
b. -67.5, -96
c. 50, -96
Answer by vleith(2983)   (Show Source):
You can put this solution on YOUR website! 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
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