These are optimization problems: 1. David and his friend will be spreading posters around the city to advertise their Halloween maze. The posters must all have an area of 200 in 2 . There must be...

These are optimization problems: 1. David and his friend will be spreading posters around the city to advertise their Halloween maze. The posters must all have an area of 200 in 2 . There must be non-printing borders on this poster: 1 inch on the left and right, and 2 inches on top and bottom. What dimensions should th eposters be to maximize the printable area? 2. There will be a room in a maze where people must crawl through. The room will be closed all around with hidden secret entrance and exit doors. The sides, front, and back of this room are to be made of mirrors that cost $6/ft 2 and the top and bottom are to be made of glow-in-the-dark ghost fabric that costs $10/ft 2 . The room needs a fixed volume of 70ft 3 , and the length of the room must be three times the width. Find the dimensions of the room which yield the cheapest cost. 3. In another room, there is a heard of zombies each person must run through to get to the exit door. The zombies slow people down, so they are on average able to run only 3mph instead of their normal 6mph. Once they reach the edge of the room, they can run without obstacle. If the room is 0.2 miles wide by 0.5 miles long, how far down the room must people run through the zombies to minimize their time in the room? 4. In the second to last room, fake blood will be dropped in front of people before they reach the end of the room. The blood is to be stored in cylindrical containers with no top. The containers need to hold 1.5 liters (1500 cm 3 ). Find the dimensions that make the cheapest production cost for each can. 5. To be good sports, David and his friend will have an abundance of candy for anyone who makes it through the maze. They have several rectangles of cardboard from which they will make boxes to hold the candy. To make these boxes they will cut squares out of the corners of the cardboard and fold up the sides to make an open-topped box. If the cardboard has original dimensions of 14 x 10 inches, what length must they cut out of the corners to make the largest volume of candy? How much room will they have for candy?