feasible region question, help please

[Navyguy]

The feasible region of a maximization problem shown is determined by
12x+5y<=180
5x+4y<=98
x^3 0, y=>0

Which of the following objective functions has its maximum value at (15,0)? My answer is z=45x+15y from a list of possible answers, is this right. If not please someone show me how to se this up or graph please. My text book shows you how but this is hard to follow. Thanks very much for understanding.

a.z=25x+25y
b.z=9x+6y
c.z=20x+10y
d.z=45x+15y

 

[tkhunny]

Graph these:

y = 36 - (12/5)x
y = (49/2) - (5/4)x

Look at the slope of these:

a.z=25x+25y ==> -1
b.z=9x+6y ==> -3/2
c.z=20x+10y ==> -2
d.z=45x+15y ==> -3

Which one is steeper than -12/5? Why does that answer the question?