A rectangular poster is to contain 162 square inches of print. the margins at the top and bottom of the poster are to be 2 inches, and the margins on the left and right are to be 1 inch. what should the dimensions of the poster be so that the least amount of poster is used?
Accepted Solution
A:
Let H ------------> the height of the printed area W -----------> the width of the printed area Then we know that HW = 162-------> H=162/W-----------> equation 1 the area of the poster is given by A = (H + 4)*(W + 2)-----------> equation 2
I substitute 1 in 2
A=([162/W] + 4)*(W + 2)-----> A=162+324/W+4W+8 By taking the derivative, Let A1------> derivative of A we have
A1 = −324/W² + 4 By setting A1 to 0, we have W²=324/4-------> W²=81------------> W=9 in H=162/W----> 162/9-----> H=18 in
the dimensions of the poster are (H + 4)-------> 18+4-----> 22 in (W + 2)------> 9+2------> 11 in
the answer is the dimensions of the poster are 11 in x 22 in