4. Page Layout Design

A graphic designer is working to optimize the layout of a multi-page print advertisement. Each rectangular page must contain 100 square inches of print. The margins at the top and bottom of the page are to be 1.5 inches deep and the margins on each side are to be 1 inch wide. The goal is to determine the dimensions of each page so that the minimum amount of paper is used.

a) Sketch a diagram of a page, showing the printed area with relevant dimensions and labeling the width, W, and the length, L.

b) Using the information above, express the length, L, in terms of the width, W.

c) Write a function for the total page area, A(w), in terms of w only. Simplify this function.

d) What is themathematical domainof this function? Explain this domain in the problem context.

e) What is thepractical(appropriate)domainof this function (appropriate to the problem context)?

f) Graph this function by finding the x and y intercepts, vertical asymptote, and a sign chart for the function. The end-behaviour of this function will be unusual – explain why this is the case. Calculate and plot some points in the appropriate domain of this function to refine the accuracy of your graph.

g) From your graph,the value of the page width that results in the minimum page area. Then calculate the corresponding page length.estimate