PLEASE ANSWER ALL THE QUESTIONS FOR A LIKE

Example 2: Variation of the Goat Enclosure Problem: Suppose now that one side of the goat enclosure is provided by the wall of the barn on the property. Hence, the 200 m of fencing is for the remaining three sides of the enclosure. What are the dimensions of the optimal goat enclosure under these conditions? Example 3: A man decides to jog to the local donut shop for breakfast. He starts at his home, point A, and jogs directly to the east to point 0. Along this path, there is a trail made for running. From point O, he then jogs directly north to get to the donut shop along a big field. If the donut shop is located 2 miles east and 1 mile north of the man's home, then answer each of the following questions: (a) The man jogs at 10 miles/hour on the road from point A to point O (on the trail) but only 6 miles per hour from point to the donut shop (in the field). Find the time it would take to the man to reach the donut shop if he takes the route given above. (b) Suppose that the man instead decides to jog directly from point A to the donut shop (in a straight line) through the field. How long would it take him to do this? (c) Suppose that the man does this every Saturday. After doing this for a couple of months, he starts to realize that while he is jogging, he just craves the donuts. He gets an idea that perhaps there is a shortest route to take. He decides that he will start trying different paths. He will jog along the trail to some point before O, then cut across the field to the donut shop. At what point should the man enter the field in order to reach the donut shop in minimum time? Example 2: Variation of the Goat Enclosure Problem: Suppose now that one side of the goat enclosure is provided by the wall of the barn on the property. Hence, the 200 m of fencing is for the remaining three sides of the enclosure. What are the dimensions of the optimal goat enclosure under these conditions? Example 3: A man decides to jog to the local donut shop for breakfast. He starts at his home, point A, and jogs directly to the east to point 0. Along this path, there is a trail made for running. From point O, he then jogs directly north to get to the donut shop along a big field. If the donut shop is located 2 miles east and 1 mile north of the man's home, then answer each of the following questions: (a) The man jogs at 10 miles/hour on the road from point A to point O (on the trail) but only 6 miles per hour from point to the donut shop (in the field). Find the time it would take to the man to reach the donut shop if he takes the route given above. (b) Suppose that the man instead decides to jog directly from point A to the donut shop (in a straight line) through the field. How long would it take him to do this? (c) Suppose that the man does this every Saturday. After doing this for a couple of months, he starts to realize that while he is jogging, he just craves the donuts. He gets an idea that perhaps there is a shortest route to take. He decides that he will start trying different paths. He will jog along the trail to some point before O, then cut across the field to the donut shop. At what point should the man enter the field in order to reach the donut shop in minimum time