Acidled Rates and Optimization: Problem 5 point) A fence is to be built to enclose a rectangular area of 320 square feet. The fence along three sides is to be made of material that costs 3 dollars per foot, and the material for the fourth side costs 14 dollars per foot. Find the dimensions of the enclosure that is most economical to construct. Dimensions: Preview My Answers Submit AnswersODIen 2 A street light is at the top of a 10 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. How fast is the tip of her shadow moving along the ground when she is 35 ft from the base of the pole? ft/sec How fast is the length of her shadow increasing? ft/sec Note: You can earn partial credit on this problem.Rates and Optimization: Problem 3 (1 point) At noon, ship A is 136 km west of ship B. Ship A is sailing east at 20 km/h and ship B is sailing north at 12 km/h. How fast is the distance between the ships changing at 2 P.M. The distance between the ships is ? at a rate of | km/h. Note: You can earn partial credit on this problem.(Once you have their money, never give it back.) An apartment complex on Ferenginar with 540 units is currently fully occupied. The current rent for a unit is 3204 slips of gold-pressed latinum. The owner of the complex knows from experience that he loses one occupant every time he raises the rent by 6 slips of latinum. Since "profit is its own reward", the owner wants to maximize his profit so he asks for our help, even though he knows that "free advice is seldom cheap" What should be our recommendation for the optimal rent? Answer: |slips of gold-pressed latinum. What is the largest revenue that the owner can earn? Answer: slips of gold-pressed latinum. Note: YouJoe is on the bank of a river that is 50 m wide and he wants to reach a point, P, located 400 m downstream on the other side. Joe can swim - m/s and run - m/s, and he will swim diagonally across the river to a point Q and then run along the (straight) river bank to P. In this question, we shall take steps to find out how Joe can reach the point P as quickly as possible. (a) Suppose that @ is located a m downstream, and let us denote the point directly across the river from where Joe is by R. For what distance will Joe swim? run? Express your answers in terms of z. Answers: Joe will swim m, and will walk m, where 0