Please help solve the following problems:

1. A farmer with 750 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible area of the four pens? What quantity is to be optimized? What parameter would we like to use? What is the domain of the parameter?2. A baseball team plays in a stadium that holds 55,000 spectators. With the ticket prices at $10, the average attendance had been 27, 000. When ticket prices were lowered to $8, the average attendance rose to 33, 000. (a) Find the demand function, assuming it is linear. (b) How should the ticket prices be set to maximize revenue?3. A manufacturer needs to make a cylindrical can that will hold 1 liter (or 1000 em ) of liquid. Determine the dimensions of the can that will minimize the amount of material used in its construction.13. A rectangular area is to be enclosed by a wall on one side and fencing on the other three sides. If 18 meters of fencing are used, what is the maximum area that can be enclosed? (A) 81 N/D m (B) m (C) 27 m2 (D) 40 m 81 (E 2 m.X. 18. The points (3, 0), (x, 0), x, - ), and (3. ) are the vertices of a rectangle, where x 2 3, as shown in the figure above. For what value of x does the rectangle have a maximum area? (A) 3 (B) 4 (C) 6 (D) 9 (E) There is no such value of x.n. Find the paint [lay] an the graph nfy = V? nearest the point [LEI]. 7. A man launches his boat from point A on a bank of a straight river, 3 km wide, and wants to reach point B, 8 km downstream on the opposite bank, as quickly as possible. He could row his boat directly across the river to point C and then run to B, or he could row directly to B, or he could row to some point D between C and B and then run to B. If he can row 6 km/h and run 8 km/h, where should he land to reach B as soon as possible? (We assume that the speed of the water is negligible compared with the speed at which the man rows.) 3 km C D