y X X A rancher has 600 feet of fencing with which to construct adjacent, equally sized rectangular pens as shown in the figure above. What dimensions should these pens have to maximize the enclosed area? C = 75 y = 100 Maximum area = 7500A rectangular storage container with an open top is to have a volume of 10 cubic meters. The length of its base is twice the width. Material for the base costs 15 dollars per square meter. Material for the sides costs 8 dollars per square meter. Find the cost of materials for the cheapest such container. Total cost = (Round to the nearest penny and include monetary units. For example, if your answer is 1.095, enter $1.10 including the dollar sign and second decimal place.)The manager of a large apartment complex knows from experience that 110 units will be occupied if the rent is $448 per month. A market survey suggests that, on the average, one additional unit will remain vacant for each $7 increase in rent Similarly, one additional unit will be occupied for each $7 decrease in rent. (Round your answers to the nearest unit cent, but do not round until your final computation.) a. If x is the number of units rented, and p is the rent per unit in dollars, what is the price-demand equation (assuming linear)? pac = b. What is the monthly revenue function for the manager? R(x) = c. How many apartment units should be rented to maximize the monthly revenue? Apartment units: d. What is the maximum monthly revenue for the manager? Maximum revenue: $ e. What rent should the manager charge to maximize the monthly revenue?d. II @ is the number of units rented, and p is the rent per unit in dollars, what is the price-demand equation (assumin linear)? p(x) = b. What is the monthly revenue function for the manager? R(x) = c. How many apartment units should be rented to maximize the monthly revenue? Apartment units: d. What is the maximum monthly revenue for the manager? Maximum revenue: $ e. What rent should the manager charge to maximize the monthly revenue? Rent: $ per unit4 attempts remaining. A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 49 feet? (Round your answer to three decimal places if necessary, but do not round until your final computation.) Area: ft 2Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Springfield and Shelbyville. There needs to be cable connecting Centerville to both towns. The idea is to save on the cost of cable by arranging the cable in a Y-shaped configuation. Centerville is located at (11, 0) in the xy-plane, Springfield is at (0, 6), and Shelbyville is at (0, -6). The cable runs from Centerville to some point (x, 0) on the x-axis where it splits into two branches going to Springfield and Shelbyville. Find the location (x, 0) that will minimize the amount of cable between the three towns and compute the amount of cable needed. (Round your answers to three decimal places if necessary, but do not round until your final computation.) a. To solve, we need to minimize the following function of x. f (20 ) = b. We find that f(x) has a critical x-value, denoted xc. Cc c. To verify that f(a) has a minimum at this critical number, we compute the second derivative f"(x) and find that its value at the critical number. number f" (xc) = is a ? d. Finally, we compute the minimum length of cable needed.a. To solve, we need to minimize the following function of x. f(a) = b. We find that f(x) has a critical x-value, denoted xc. Cc c. To verify that f(a) has a minimum at this critical number, we compute the second derivative f"(a) and find that its value at the critical number. f"(xc) is a ? number d. Finally, we compute the minimum length of cable needed. f(xc )A wire of length 14 is cut into two pieces which are then bent into the shape of a circle of radius r and a square of side s. Then the total area enclosed by the circle and square is the following function of s and r If we solve for s in terms of r, we can reexpress this area as the following function of r alone: Thus we find that to obtain maximal area we should let r = To obtain minimal area we should let rA printed poster is to have a total area of 501 square inches with top and bottom margins of 3 inches and side margins of 2 inches. What should be the dimensions of the poster so that the printed area be as large as possible? (Round your answers to three decimal places if necessary, but do not round until your final computation.) a. To solve, let x denote the width of the poster in inches and let y denote the length in inches. We need to maximize the following function of a and y. Area in terms of a and y: 501 b. We can reexpress this as the following function of x alone. f ( ac) = c. We find that f(x) has a critical x-value, denoted xc. d. To verify that f(x) has a maximum at this critical number we compute the second derivative f"(x) and find that its value at the critical number. is a ? O number f(xc ) = e. We determine the optimal dimensions of the poster. Customize Chromeb. We can reexpress this as the following function of x alone. f (3) = c. We find that f(x) has a critical x-value, denoted cc. Cc d. To verify that f(a) has a maximum at this critical number we compute the second derivative f"(a) and find that its value at the critical number. f (* ) is a ? & number e. We determine the optimal dimensions of the poster. inches by y inches f. Finally, this gives us a maximumal printed area. Area: square inchesFind the points on the ellipse 4x2 + y? = 4 that are farthest away from the point (1, 0). List them as a list of points, such as " (1, 2), (3,4) ". List of points: ( - 3 ).(43 2 A