Ella Mental has $600$ ft of fencing to enclose two fields. One is to be a rectangle twice as long as it is wide and the other is to be a square. The square field must contain at least $100$ ft squared. The rectangular one must contain at least $800$ ft squared.
a. If $x$ is the width of the rectangular field, what is the domain of $x$?
b. Plot the graph of the total area contained in the two fields as a function of $x$.
c. What is the greatest area that can be contained in the two fields? Justify your answer
By the way, the answers to a, b, c are...(according to the textbook)
a. domain: $20\le x\le 93.333333\dots$
b. $A(x) = 22500 -450x + 4.25x$ squared
c. greatest area $= 17522.2222$
I keep getting the wrong answer for the greatest area. Please provide me with explanations to each