Optimal Foraging Using data collected by zoologist Reto Zach, the work done by a crow to break open a whelk (large marine snail) can be estimated by the function 20 W = (1 + H - 0.93) where H is the height (in meters) of the whelk when it is dropped. Source: The Mathematics Teacher. (a) Find dW/dH. (b) One can show that the amount of work is minimized when dWldH = 0. Find the value of H that minimizes W. (c) Interestingly, Zach observed the crows dropping the whelks from an average height of 5.23 m. What does this imply?

Optimal Foraging Using data collected by zoologist Reto Zach, the work done by a crow to break open a whelk (large marine snail) can be estimated by the function 20 W = (1 + H - 0.93) where H is the height (in meters) of the whelk when it is dropped. Source: The Mathematics Teacher. (a) Find dW/dH. (b) One can show that the amount of work is minimized when dWldH = 0. Find the value of H that minimizes W. (c) Interestingly, Zach observed the crows dropping the whelks from an average height of 5.23 m. What does this imply?

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.1: Quadratic Functions

Problem 63E: Maximizing land area Jake has 800 feet of fencing to enclose a rectangular plot of land that borders...

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Use your schools library, the Internet, or some other reference source to find the real-life applications of constrained optimization.
Maximizing storage are A farmer wants to partition a rectangular feet storage are in a corner of his barn, as shown in the illustration. The barn walls from two sides of the stall, and the farmer has 50 feet of partition for the remaining two sides. What dimensions will maximize the area?
Maximizing land area Jake has 800 feet of fencing to enclose a rectangular plot of land that borders a river. If Jake doesnt need a fence along the side of the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed?
A page that is x inches wide and y inches high contains 30 square inches of print. The top and bottom margins are each 1 inch deep and the margins on each side are 2 inches wide (see figure). (a) Show that the total area A of the page is A=2x(x+11)x4 (b) Determine the domain of the function based on the physical constraints of the problem. (c) Use a graphing utility to graph the area function and approximate the dimensions of the page that use the least amount of paper. Verify your answer numerically using the table feature of the graphing utility.