1. [-/1 Points] DETAILS Math 110 Course Resources Optimization Course Packet on applications: Maximizing the area of an enclosed field A rectangular field is to be enclosed by 460 feet of fence. One side of the field is a building, so fencing is not required on that side. Fenced Area Building Determine the dimensions of the rectangle that maximize its area. Length of side perpendicular to the building, x = feet Length of side parallel to the building = feet OCT 19 City 4 esc F1 F2 F3 988 F4 F5 F7 DII F F9 # A & 3 4 5 6 8 O Q W E R T Y U O A S D F G H J K Z X C V B N M 98 option command2. [l1 Points] DETAILS . 1 MY NOT! A billboard designer has decided that a sign should have S-ft margins at the top and bottom and 1-ft margins on the left and right sides. Furthermore, the billboard should have a total area of 4500 ft2 (including the margins). i Printed Region ' P _J i777 , ~77 I If x denotes the left-right width (in feet) of the billboard, determine the value of x that maximizes he area of the printed region of the billboard. Use this value of x to compute the maximum area of the printed region. Maximum area of printed region : {:i square feet / 3. [-I1 Points] DETAILS [ By cutting away an x-byx square from each corner of a rectangular piece of cardboard and folding up the resulting flaps, a box with no top can be constructed F14 er4 If the cardboard is 12 inches long by 12 inches wide, determine the value of x that yields the maximum volume of the resulting box. Use this value of x to compute the maximum volume of the box. Maximum volume of box = l:' cubic inches 4. [I1 Points] DETAILS I MYNO' Math 110 Course Resources - Optimization Course Packet on applications: Minimizing the cost of construction A rectangular box is to have a square base and a volume of 72 ft3. ' ' 2 cents ers uare foot, If the material for the base costs 10 cents per square foot, material for the tap costs 54 cents per square fogs, arggthne 3::223 for the stdes costs 1 p q determine the dimensions of the box (in feet) that minimize the total cost of materials used In constructing e g . Height of the box, y = feet Width of the base, x = [:l feet