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1 112 Advanced ( ) Due: Mon Apr :00 AM MDT Question /5

2 1. Question Details MinMax Full Choice 3 sp15 [ ] A corral is to be built by joining three sides of a rectangle to a semicircle as shown figure below. The diameter of the semicircle is the same as one side of the rectangle. The lengths x and y are variable. Suppose that the total amount of fencing used is 500 feet. Follow the steps to maximize the enclosed area. a. Write the formulas for the amount of fencing and the enclosed area in terms of x and y. Enter as exact formulas. Use π as needed. Enclosed Area: A = Amount of Fencing: F = b. What are the objective function (stated first) and constraint equation (given second) for this problem? (You only get 2 attempts.) The amount of fencing, given that the area is 500. The enclosed area, given that the amount of fencing is 500. The enclosed area, given that the diameter of the circle is 500. The enclosed area, given that the height of the rectangle is 500. c. What would you set equal to zero to find the length that maximizes area? Select all that apply. (You only get 5 attempts.) A If the constraint was solved for x F If the constraint was solved for y df dx da dx df dy da dy if the constraint equation was solved for y. if the constraint equation was solved for y. if the constraint equation was solved for x. if the constraint equation was solved for x. d. What is the largest possible area you can enclose? Be accurate to the nearest whole number. Include correct units. Maximum Area = 2/5

3 2. Question Details MinMax Formula 9 sp15 [ ] An area is formed by joining a right triangle to the end of a rectangle as shown. The dimensions of the rectangle are variable and given by x and y. The right triangle's legs are of both equal to the height of the rectangle y. What are the dimensions that maximize the enclosed area if the perimeter is 400 feet? Round answers to the nearest one decimal place. y = x = 3. Question Details MinMax Formula 10 [ ] A box has two square sides and one open rectangular face, as shown in the figure below. Suppose that the volume of the box is a fixed but unknown constant, V. What dimensions would require the smallest amount of material? Give exact symbolic answers in terms of V. x = y = Which statement is true for the box using the minimum amount of material? x is bigger than y. y is bigger than x. 3/5

4 4. Question Details My Pipe MinMax 1 [ ] Suppose you have to run a pipe from point A to point C at the corners of the rectangular field shown below. You have three choices for how to do this. Option 1. Bury the pipe in a trench that goes diagonally from A to C. Option 2. Bury the pipe in a trench from A to B. Then run it above ground from B to C. Option 3. Pick a point, P, somewhere between B and C. Bury the pipe in a trench that goes from A to P. Then run it above ground from P to C. This is the plan shown in the figure. All distances shown are measured in feet. The cost to bury pipe is $150 per foot. The cost to run the pipe above ground is $82 per foot. How much will Option 1 cost? Round to the nearest dollar. How much will Option 2 cost? Round to the nearest dollar. How much will Option 3 cost if P is located at x = 10 feet? Round to the nearest dollar. How much will the cheapest possible option cost? Round to the nearest dollar. 5. Question Details My Pipe MinMax 2 [ ] Suppose you have the same pipe problem as before, but this time the costs are $150/ft to bury the pipe and $140/ft to run it above ground. How much will the cheapest option cost? Round to the nearest dollar. Cheapest pipe cost = Assignment Details Name (AID): 112 Advanced ( ) Submissions Allowed: 100 Category: Homework Code: Locked: Yes Author: Skriletz, Jaimos ( jaimosskriletz@boisestate.edu ) Last Saved: Mar 17, :05 PM MDT Feedback Settings Before due date Question Score Assignment Score Publish Essay Scores Question Part Score Mark 4/5

5 Group: BSU Calculus Randomization: Person Which graded: Last Help/Hints Response Save Work After due date Question Score Assignment Score Publish Essay Scores Key Question Part Score Solution Mark Add Practice Button Help/Hints Response 5/5