The objective function is z=ax+by with maximum value 180 occurring at points (15,15) and (0,20).
Since the maximum value is 180 at point (15,15):
z=ax+by
180=a(15)+b(15)
180=15a+15b
12=a+b ... ①
Since the maximum value is also 180 at point (0,20):
z=ax+by
180=a(0)+b(20)
180=20b
b=9 ... ②
From equation ①:
a+b=12
a+9=12
a=3
Therefore, a=3 and b=9.
The answer is option 1.