2. You are under contract to design a storage building with a square base and a volume of 14,000 cubic feet. The cost of materials is $4 per square foot for the floor, $16 per square foot for the walls and $3 per square foot for the roof. Find the dimensions that minimize the cost of materials.

2. You are under contract to design a storage building with a square base and a volume of 14,000 cubic feet. The cost of materials is $4 per square foot for the floor, $16 per square foot for the walls and $3 per square foot for the roof. Find the dimensions that minimize the cost of materials.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

ChapterP: Prerequisites

SectionP.FOM: Focus On Modeling: Making The Best Decisions

Problem 5P: Edging a Planter A woman wants to make a small planter and surround it with edging material. She is...

See similar textbooks

Related questions

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: By using implicit differentiation to find an equation of the tangent line to the curve at the given…

Q: X y a= 1 884 2 1149 3 1618 4 5 2190 2962 6 3705 Use regression to find an exponential equation that…

A: Given Table : X Y 1 884 2 1149 3 1618 4 2190 5 2962 6 3705 .

Q: Question 1 Given the graph of y=f(x) in the diagram, sketch the graphs of its first and second…

A: Solve the following

Q: 40 30- 20- Population of Canada, 1881 to 2011

A: From the graph we can conclude as

Q: If y = 1 when x = 0, solve the differential equation 2x + cos(x) 6y² dy dx =

A: First separate the variables x and y then integrate both sides to solve this differential equation.

Q: Write the equation of the line in the point-slope form that passes through the points (0,8) and…

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Find the limit. lim (3x)² = (Type +0<x (Type an exact answer.)

Q: Problem #1: In a murder investigation, the temperature of the corpse was 36°C at 1:30pm and 19°C 3…

A: Solution: Given data, let t = 0(hrs) be 1:30 p.m. T(t) body temperature at time t T(0) = T₀ = 36°C…

Q: The table below shows the value, V, of an investment (in dollars) after n years. n 3 7 12 14 19 0…

A: Solution: By using exponential regression graph plotter

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

Q: 2. xy=-x³y-csc (xy)

A: Given differential equation:- x4y'=-x3y-cscxy

Q: How many possible real negative zeros are there for the function f(x) = 4x4 - 5x³+x² - 4x +1? A 0 B…

A: The given function is: fx=4x4-5x3+x2-4x+1 To find: How many possible real negative zeros are there…

Q: Given Cost and Revenue functions C(q)=q3−11q2+55q+5000 and R(q)=−3q2+2400q, what is the marginal…

Q: For each number line problem below, identify the computation it models. (Select all that apply.) (а)…

A: To Find : Computation it models through given figure

Q: 3. Determine whether Rolle's Theorem can be applied to Ax) = -x² + 10x on the closed interval…

Q: Use the equations m = (Σ*k) (Σγκ) - η Σ×κυκ -n and b = n (Ek-mΣxx) with all sums running from k = 1…

Q: According to a study, a vehicle's fuel economy, in miles per gallon (mpg), decreases rapidly for…

Q: Consider the following graph of the second derivative, f" (x), for some function f(x): f"(x) -6 -4…

Q: Find dv/dx by implicit differentiation, given that -x^2/v^2-cos(3v)=-8

Q: d dx Prove that (csc(x)) = -csc(x) cot(x). d dx (csc(x)) = || = = d dx sin²(x) 1 sin(x) 1 -csc(x)…

Q: A price index was approximately 98.6 (base year 1992) at the beginning of 1991. If inflation…

A: Formula used A = P( 1 + R100 )t A = amount after time t P = initial amount R = rate

Q: The equation A(t) = 2000e0.045t gives the balance after t years of an initial investment of 2000…

A: Equation given A(t) = 2000e0.045t Find - (1) dA/dt(2) Find and intepret A'(5)(3) compare the…

Q: A street light is mounted at the top of a 15ft tall pole. A man 6ft tall walks away from the pole…

Q: solve it by hand step by step expline each steps dx dt dy dt = 3x(t) - 4y(t) + 1 = 4x(t)-7y(t) + 10t

A: The answer is in step 2.

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

Q: 10. For the function f(x) = x³ 3x² - 9x (a) Find the intercepts. Show work. Round to two decimal…

Q: 9. The measurement of the side of a square floor tile is 14 inches, with a possible error of 78…

A: Measurement of the side.

Q: For the formula at the given point, find the equation of the tangent line 5. y=x²e at the point…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: Throughout this problem, consider R to be the region between the curves f(x) = 2x and g(x) = x³ in…

Q: Use l'Hôpital's Rule to find the limit. In (x²+7x) In x lim X→0* lim X→0* In (x² +7x) In x = (Type…

A: K=limx→0+lnx2+7xlnxd dx(xn)=nxn-1d dx(lnx)=1x

Q: Differentiate. Step 1 F(y) x) = (1/²2 - 11/2) (v + 8y²³) To find the derivative of the product F(y)…

A: The given data is: Differentiate Fy=1y2-4y4y+8y3

Q: Sketch the region of integration and change the order of integration. *9 *√81 - y² 1₁ 0 -9 JO f(x,…

A: The given integral is:∫-99∫081-y2 f(x,y) dx dy

Q: Find the gradient of the function at the given point. Function Point f(x, y, z)=√√√x² + y² + z² (2,…

Q: Use l'Hôpital's Rule to find the following limit. 5x² lim x→0 In (sec x) 5x² lim x→0 In (sec x) 11…

Q: 1 I 1 1 1 1 I I 1 I 1 1 1 1 I 1 1 1 I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 1 1 1 1 I I I…

Q: Use the given feasible region determined by the constraint inequalities to find the maximum and…

Q: f(91+ (9t + 2)²/3 dt

Q: Calculate the double integral. ₂ yexy dA, R R= [0, 2] × [0, 5]

Q: The demand for a new computer game can be modeled by p(x) = 55-4 Inx, for 0≤x≤800, where p(x) is the…

Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

Q: Please help me with every question :)

A: Here we have to choose the correct option.

Q: Solve the given differential equation. dy + In xy dx = (10x + In y)dx y=0

Q: 3 Find the open intervals where the function f(x) = -2x³ + 6x² +171x-2 is concave upward or concave…

A: given function is :-f(x) = -2x3+6x2+171x-2then we have to find point of inflection and concavity…

Q: Use Lagrange multipliers to prove that the rectangle with maximum area that has a given perimeter p…

Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y)=6ey-3ye* Select…

A: The function is given as , fx,y=6ey-3yex find all local maxima , local minima and saddle points.

Q: In 2012, U.S. consumption of renewable energy was 8.45 quadrillion Btu. Since the 1960s, consumption…

A: Solution: Given: f′(t) = 0.004t + 0.062 To find f(t), we need to integrate the given rate of growth…

Q: 1. For the function y = 2x²-3x use a simplified algebraic expression in terms of a and h to estimate…

Q: 2. Find f'(1) if f(x) = 3x³ (√x-2).

Q: 11. A rectangular page is to contain 144 square inches of print. The margins on each side are 1…

Question

TYPEWRITTEN

Direction: Analyze the given problem. Show your complete and detailed solution (Given, Unknown, Solution,
and Answer).
2. You are under contract to design a storage building with a square base and a volume of 14,000 cubic
feet. The cost of materials is $4 per square foot for the floor, $16 per square foot for the walls and $3
per square foot for the roof. Find the dimensions that minimize the cost of materials.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Edging a Planter A woman wants to make a small planter and surround it with edging material. She is deciding between two designs. Design 1: A square planter Design 2: A circular planter Edging material costs 3 a foot for the straight variety, which she would use for design 1 and 4 a foot for the flexible variety, which she would use for design 2. a If she decides on a perimeter of 24 ft, which design would give her the larger planting area? b If she decides to spend 120 on edging material, which design would give her the larger planting area?
Gardening A gardener wishes to enclose her rectangular raspberry patch with 40 feet of fencing. The raspberry bushes are planted along the garage, so no fencing is needed on that side. Find the dimensions if the total area is to be 192 feet.
When solving a uniform motion problem, how does creating a table help you?
A garden has 60 yards of fencing and wants to enclose a rectangular garden that requires fencing only on three sides. Find the length and width of the plot that will maximize the area.
When solving a uniform motion problem, how does drawing a diagram of the situation help you?
The manufacturer of a weight training bench spends $15 to build each bench and sells them for $32. The manufacturer also has fixed costs each month of $25,500. (a) Find the cost function C when x benches are manufactured. (b) Find the revenue function R when x benches are sold. (c) Show the break-even point by graphing both the Revenue and Cost functions on the same grid. (d) Find the break-even point. Interpret what the break-even point means.
The Turners want to install outdoor carpet around their rectangular pool. The dimensions for the rectangular area formed by the pool and its walkway are 20 ft by 30 ft. The pool is 12 ft by 24 ft. aHow many square feet need to be covered? bApproximately how many square yards does the area in part a represent? cIf the carpet costs 12.95 per square yard, what will be the cost of the carpet?
Sue wants to build an enclosed area behind her house for her pets. One wall of the enclosed area will be the back of her house. She needs to the total area to be 90 square feet. She wants to minimize the cost of the fence materials. For the sides, W, fence materials cost $3 /ft; for the length, L, they cost $5 /ft. What dimensions should the fence be?
An offshore oil well is 2 kilometers off the coast. The refinery is 6 kilometers down the coast (see figure). Laying pipe in the ocean is twice as expensive as on land. What path should the pipe follow in order to minimize the cost?
a. Find the number of bicycles that must be manufactured to minimize the cost. b. Find the cost
A telephone company needs to lay cable from one of its owners to a small island that is offshore. It cost the company $10,000 per mile to lay the cable on land, and $15,000 per mile to lay the cable through the water. What is an equation that needs to be optimize to find the minimum cost?
A rancher plans to use an existing stone wall and the side of a barn as a boundary for two adjacent rectangular corrals. Fencing for the perimeter costs 10 per foot. To separate the corrals, a fence that costs 8 per foot will divide the region. The total area of the two corrals is to be 7,000 square feet. Use Lagrange multipliers to find the dimensions that will minimize the cost of the fencing.