Question

Traffic Signal (A)* Calculus Emphasis: Optimization Skills Emphasized: Pythagorean Theorem, derivative over a closed interval. The Problem. A small town wishes to hang a traffic signal at an intersection according to the following parameters. I. The top of the traffic signal must be 18 feet above the ground. 2. The traffic light will hang between two 40-foot tal buildings using cables according to the diagram shown below . The two buildings are 30 feet apart. 30 ft What is the minimum total length of cable required to hang the traffic light? (Assume all connections are individual points.) Nearly all calculus textbooks contain fencing problems This problem puts that type of problem in a real-life context Farms often contain various types of animals which need to be separated by individual pens. Suppose a farm has bulls, steers, calves, heifers, milk-cows with calves, and cows just for milking. Bulls aren't near the heifers because it riles them up, cows which have calves have their milk reserved for their babies. Colostrum is the first milk produced by the cows after they have their babies. It's some of the most nutrient dense milk you can find. It's filled with beneficial immunoglobulins, growth factors, and antibodies that promote a healthy immune system, and also oligosaccharides that promote healthy bacteria growth in the calves' digestive system. A pen configuration that accommodates these criteria and could look like this A farmer has $10,560 to construct the pens as shown. The four sides of the Bull's pen costs $12 per linear foot and all other fence lengths cost $8 per linear foot. What would be the dimensions of each animal's pen if we want to maximize the total area of the penned region?

Answer 1

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