We are given that the objective function Z = ax + by has maximum value 42 at (4, 6) and minimum value 19 at (3, 2).
We can use these two points to form a system of two equations in two unknowns a and b as follows;
42 = 4a + 6b & 19 = 3a + 2b
On solving above equations, we get
a = 3 & b = 5