1. A hotel with 300 rooms is filled to capacity every night if they charge $80 per room per night. For each $1 increase in room rental rate, they rent out 3 fewer rooms per night. Each rented room also costs the hotel $10 to service each morning. First, construct a Profit function using x = number of room rate increases. Then complete the following: a) The new price per room each night b) How many rooms will be rented each night c) Maximum Profits per night 2. A supplier of bolts wants to create open boxes for the bolts by cutting a square from each corner of a 12 in by 12 in piece of metal and then folding up the sides. What size square should be cut from each corner to produce a box of maximum volume? 3. A three sided fence is to be built next to a straight river which forms the fourth side of a rectangular region. The enclosed area is to equal 3200 square feet. The cost of the fence is $2 per ft. Find the dimensions that minimize the cost of the fence. 4. A square-based, box-shaped shipping crate is designed to have a volume of 16ft3. The material used to make the base costs $2.00 per square foot, the material used in the sides costs $1.00 oer square foor, and the material used to make the top costs $0.50 per square foot. What are the dimensions of the crate that minimize the cost of the materials