3. [15 pts] You would like to make a poster that will have a total area of 400 in² and will
have 0.5 inch margins on the sides, a 3 inch margin on the top and a 1 inch margin on
the bottom as shown below. Let $w$ and $h$ represent the width and height, respectively,
of the poster. For this problem, you will determine the dimensions that will give the
largest printed area.
(a) What is the objective function in terms of $w$ and $h$?
(b) What is the constraint equation?
(c) Write your objective function as a function of only $w$.
(d) What is the domain of your function?
(e) Differentiate your function and identity all critical
numbers.
(f) Find the value of $w$ that maximizes your objective
function (be sure to justify your answer).
(g) State the width and height that give the largest printed
area. What is the largest printed area? Provide units
with your three answers.