OptimizationAnswer the following optimization problems systematically. Show your solution.a. An open box is to be made from a 16 cm by 30 cm piece of cardboard by cutting out squares of equal size from the four corners andbending up the sides. How long should the sides of the squares be to obtain a box with the largest volume?b. A rectangular box is to be made from a piece of cardboard 24 cm and 9 cm wide by cutting out identical squares from the four cornersand turning up the sides. Find the volume of the largest rectangular box that can formed.

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Answered: An open box is to be made from a 16 cm…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.4: Linear Programming

Problem 23E

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Size of High Schools The farm population has declined dramatically in the years since World War II, and with that decline, rural school districts have been faced with consolidating in order to be economically efficient. One researcher studied data from the early 1960s on expenditures for high schools ranging from 150 to 2400 in enrollment. He considered the cost per pupil as a function of the number of pupils enrolled in the high school, and he found the approximate formula C=7430.402n+0.00012n2 where n is the number of pupils enrolled and C is the cost, in dollars, per pupil. a. Make a graph of C versus n. b. What enrollment size gives a minimum per-pupil cost? c. If a high school had an enrollment of 1200, how much in per-pupil cost would be saved by increasing enrollment to the optimal size found in part b?

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An open box is to be made from a 16 cm by 30 cm piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. How long should the sides of the squares be to obtain a box with the largest volume?