Posted by casidhe on .
I've posted this question before and think I've made some progress but it some part of the second answer I got is wrong
I've done the first question but I cannot get any farther. I'm so stuck. Please explain or just help me to figure out the next steps.
A printed poster is to have a total area of 837 square inches with top and bottom margins of 7 inches and side margins of 6 inches. What should be the dimensions of the poster so that the printed area be as large as possible?
*To solve this problem let x denote the width of the poster and let y denote the length. We need to maximize the following function of x and y:
*We can reexpress this as the following function of x alone:ANSWER: f(x)=(x-12)(837/x-12)+14
*We find that f(x) has a critical number at x=_________
*To verify that f(x) has a maximum at this critical number we compute the second derivative f(x) and find that its value at the critical number is_________, a negative number.
*Thus the optimal dimensions of the poster are ________ inches in width and ________ inches in height giving us a maximal printed area of ________square inches.