Final answer:
To find the maximum area inside the margins, determine the dimensions of the poster and use trial and error to find the dimensions that result in the maximum area.
Step-by-step explanation:
To find the maximum area inside the margins, we need to determine the dimensions of the poster. Let's assume the width of the poster is x inches. Since there are 1 inch margins on each side, the actual width of the region inside the margins is (x - 2) inches. Similarly, assuming the height of the poster is y inches, the height of the region inside the margins is (y - 4) inches (2 inch margins at the top and bottom).
Now, we can calculate the area of the region inside the margins by multiplying the width and height: A = (x - 2)(y - 4). Since we want to maximize the area, we need to find the maximum value of A.
To find the maximum area, we can use calculus by taking the derivative of A with respect to x and setting it equal to zero. However, in this case, since we are dealing with integers for dimensions, we can use trial and error to find the dimensions that result in the maximum area. We start by finding the dimensions that give an area of exactly 200 square inches.
For example, if we set x - 2 = 20 and y - 4 = 10, then the area is (20)(10) = 200 square inches. So, the maximum area inside the margins is 200 square inches when the width of the poster is 22 inches and the height of the poster is 14 inches.