c210 wrote:
a) they say the maximum for 20x + 10y is 250 when x=0 and y=25, why didn't they make the maximum value using x=25 , y=0 since that would give you a larger number?
b) why didn't they use option (1) and solve for Y , then plug that into X=Y=25 from the original problem? wouldn't that solve for x right away?
its probably something simple that I'm missing but any clarity would be appreciated its really bugging me!
thanks in advance!
As for your questions (notice that x and y are nonnegative integers):
A. 250 is
the smallest possible value of 20x+10y: minimize x, as it has greater multiple (20) and maximize y, as it has smaller multiple (10) --> x=0 and y=25 --> 20x +10y=250. The same way
the largest possible value of 20x+10y is for x=25 and y=0 --> 20x +10y=500.
Or another way: 20x+10y=20x+10(25-x)=10x+250 --> to get
the smallest possible value minimize x, so make it 0: 10x+250=250, and to get
the largest possible value maximize x, so make it 25: 10x+250=500.
B. You can not solve for x or y as
you get only the ranges for them from (1), as well as from (2), and not the unique values (refer to the solution above).
Hope it helps.
You taught me one hard rule, I'll never forget with inequilities. You can only add two inequalities in the same direction, never subtract!!
Now, does this rule differ if I compare an inequality to an equation? Can I subtract an inequality and an equation in the same direction?
Can I simply subtract with confidence to get: x<5? I know that I can solve for y in equation (2) and substitute in equation (1). I would appreciate if you could confirm