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A pencil cup with a capacity of 33 in.3 is to be constructed in the shape of a right circular cylinder with an open top. If the what should the radius of the base of the cup be material for the sides costs 29¢/in.2 and the material for the base costs 46c/in. to minimize the construction cost (in ¢)? Letr and h (in in.) be the radius and height of the pencil cup, respectively. in. (Round your answer to two decimal places, if necessary.) Complete the following parts. (a) Give a function f in the variable r for the quantity to be optimized. f(r) = ( cents (b) State the domain of this function. (Enter your answer using interval notation.) (c) Give the formula for h in terms of r. h = (d) To determine the optimal value of the function f, we need the critical numbers of ---Select- . (e) These critical numbers are as follows. (Round your answer(s) to two decimal places, if necessary. If a critical number is an endpoint of the domain, do NOT include it in your answer. Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) r=

A pencil cup with a capacity of 33 in.3 is to be constructed in the shape of a right circular cylinder with an open top. If the what should the radius of the base of the cup be material for the sides costs 29¢/in.2 and the material for the base costs 46c/in. to minimize the construction cost (in ¢)? Letr and h (in in.) be the radius and height of the pencil cup, respectively. in. (Round your answer to two decimal places, if necessary.) Complete the following parts. (a) Give a function f in the variable r for the quantity to be optimized. f(r) = ( cents (b) State the domain of this function. (Enter your answer using interval notation.) (c) Give the formula for h in terms of r. h = (d) To determine the optimal value of the function f, we need the critical numbers of ---Select- . (e) These critical numbers are as follows. (Round your answer(s) to two decimal places, if necessary. If a critical number is an endpoint of the domain, do NOT include it in your answer. Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) r=

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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TEACHER A pencil cup with a capacity of 33 in.3 is to be constructed in the shape of a right circular cylinder with an open top. If the material for the sides costs 29¢/in.2 and the material for the base costs 46¢/in.2, what should the radius of the base of the cup be to minimize the construction cost (in ¢)? Letr and h (in in.) be the radius and height of the pencil cup, respectively. r = in. (Round your answer to two decimal places, if necessary.) Complete the following parts. (a) Give a function f in the variabler for the quantity to be optimized. " cents (b) State the domain of this function. (Enter your answer using interval notation.) (c) Give the formula for h in terms of r. h = (d) To determine the optimal value of the function f, we need the critical numbers of --Select-. (e) These critical numbers are as follows. (Round your answer(s) to two decimal places, if necessary. If a critical number is an endpoint of the domain, do NOT include it in your answer. Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) r=
Transcribed Image Text:TEACHER A pencil cup with a capacity of 33 in.3 is to be constructed in the shape of a right circular cylinder with an open top. If the material for the sides costs 29¢/in.2 and the material for the base costs 46¢/in.2, what should the radius of the base of the cup be to minimize the construction cost (in ¢)? Letr and h (in in.) be the radius and height of the pencil cup, respectively. r = in. (Round your answer to two decimal places, if necessary.) Complete the following parts. (a) Give a function f in the variabler for the quantity to be optimized. " cents (b) State the domain of this function. (Enter your answer using interval notation.) (c) Give the formula for h in terms of r. h = (d) To determine the optimal value of the function f, we need the critical numbers of --Select-. (e) These critical numbers are as follows. (Round your answer(s) to two decimal places, if necessary. If a critical number is an endpoint of the domain, do NOT include it in your answer. Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) r=
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