A company manufactures shipping boxes with equal height and width. The area of the base of each box is at most 28 square inches. The boxes have a band that is one inch thick and that runs the length of the box. This band allows space
for printing of a company logo and other needed information. The band's area is x square inches. So, the square face needs
to be larger than this band.
Given these restrictions, the area of the square front face of the box needs to be, at minimum, 11 inches more than the area
of the band. Let the length of a box be x and the height and width of the box be y. This system of inequalities represents this
situation:
xy S 28
y2 2x+11
After we write the inequalities as equations and solve them for y, we graph each equation in the coordinate plane. The graph
looks like this: