Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 24/Solution 1

We know the absolute maximum is found on the boundary of the domain. We can also see from the function ${\textstyle f}$ and its domain that ${\textstyle x}$ has a positive coefficient, ${\textstyle y}$ has a negative coefficient, and the intervals where ${\textstyle x}$ and ${\textstyle y}$ can exist are both positive. From this we can deduct that ${\textstyle f(x,y)}$ will be maximised when ${\textstyle x}$ is at the upper bound of its domain, and ${\textstyle y}$ is at the lower bound of its domain. This is

$$f(2,0)=2(2)-3(0)=4.$$