if someone can pleaae help with these it would be amazing. please give answers for all questions and please write clear!! thank you! :)

Problem Situation: A construction company wishes to build a rectangular enclosure to store machinery and equipment The site selected borders on a river that will be used as one of the sides of the rectangle. Fencing will be needed to form the other three sides. The company has 682 feet of 10-foot high chain-link fencing. The questions that follow should help you determine the dimensions of the rectangle that will produce the maximum area for the storage site. Assume that the company wishes to use all of the fencing, and that "width" refers to the measure of each of the two sides that are perpendicular to the river, and length refers to the measure of the side parallel to the river (see diagram). For the questions that follow, all measurement answers are to be given with the correct unit label, eg. feet, square feet, etc. River width Storage Area width length PART 1 1. Copy the following table into your project and complete it, showing the dimensions (width and length) of some possible enclosures along with the resulting areas. (Recall that the company is using 682 feet of fencing total.) Width (feet) Length (feet) Area (sq. ft.) 25 50 75 100 200 225 250 275 632 582 532 482 282 232 182 132 15,800 29,100 34,900 49200 50400 52200 4550030300 2. Of all the dimensions (length and width) listed in the table, which choice gives the largest area for the enclosure? Express your answer with appropriate units. 3. Let w represent the width, and I represent the length. Recalling that there is a total of 682 feet of fencing and it is all to be used, write an equation expressing / in terms of wi.e, in the form /= 4. Write the general formula for the area A of a rectangle in terms of land w. 5. Use the general formula from Question #4 to write the area of the enclosure as a function of w (that is with function notation A(w) - ...) in "standard" form. What type of function is this? 6. Obtain a graph of the area function. Choose a window that shows both horizontal intercepts and the vertex Label the axes with variable and word labels, and label the tic marks on each axis. Look at the window on your graphing calculator to help with this. Label the graph with its function Give your graph a title. Write the window settings you used: Xmin, Xmax, Xscl, Ymin, Ymax, Yse. Locate the point on your graph that represents your answer to Question #2 by letting Y2 - the corresponding value from Question #2, then finding the intersection. Include the line for Y2 on your graph On your graph, draw an arrow pointing to the point that represents your answer to Question #2, and write the coordinates as an ordered pair Note: Is your point the maximum point on the graph or is there a slightly better width that gives a larger area? The following has you determine the maximum point graphically. 7. What do we call the graph of this area function? 8. What is the name of the point that represents the maximum area? 9. Use your calculator to find the maximum area. Indicate your process by completing the following 2 TRACE(CALC). Write down the maximum area and the required width with appropriate units. 10. What is the length of the enclosure of maximum arca? Use the appropriate unit Show the calculations using the formula from Question #3 Now find the maximum point algebraically by answering the following. 11. Find the width needed to give the maximum area algebraically. Show the formula you used and the steps to the solution. Express your answer with appropriate unit. 12. Now find the maximum area algebraically using the function 4(w) Show the substitution into A(W) Express your answer with appropriate unit. PART 2 Instead of building the enclosure of maximum area, the company wishes to build only a 50,000 square foot enclosure still using up all the fencing and situated with one side on the river. Find the dimensions of the enclosure that will satisfy these requirements by doing the following: 13. What equation can be solved to find the possible widths? 14. Use your calculator to solve this equation graphically. Obtain a graph that shows your area function and the line for the 50,000 square foot enclosure Label the axes with variable and word labels, and label the tic marks on each axis. Label each graph with its function Give your graph a title. Write the window settings you used: Xmin, Xmax, Xsel, Ymin, Ymax, Ysel. On your graph, draw an arrow pointing to the point(s) that represents your answer to this question, and write the coordinates as an ordered pair. Write your solution(s) to the nearest tenth of a foot with appropriate units. 15. Using the widths from Question #14, find the corresponding lengths. Express your answers to the nearest tenth of a foot with appropriate units. 16. In sentence form, tell the company the dimensions (length x width) that it can use to satisfy its requirements. The sentence should include dimensions to the nearest tenth of a foot with appropriate units. 17. Now support your answers that you obtained graphically by showing how to solve the equation in Question #13 algebraically. Show all steps in the solution and write the resulting widths to the nearest tenth of a foot and with appropriate unit