 4.7.1: Consider the following problem: Find two numbers whose sum is 23 an...
 4.7.2: Find two numbers whose difference is 100 and whose product is a min...
 4.7.3: Find two positive numbers whose product is 100 and whose sum is a m...
 4.7.4: Find a positive number such that the sum of the number and its reci...
 4.7.5: Find the dimensions of a rectangle with perimeter 100 m whose area ...
 4.7.6: Find the dimensions of a rectangle with area whose perimeter is as ...
 4.7.7: Consider the following problem: A farmer with 750 ft of fencing wan...
 4.7.8: Consider the following problem: A box with an open top is to be con...
 4.7.9: A farmer wants to fence an area of 1.5 million square feet in a rec...
 4.7.10: A box with a square base and open top must have a volume of 32,000 ...
 4.7.11: If 1200 cm of material is available to make a box with a square bas...
 4.7.12: A rectangular storage container with an open top is to have a volum...
 4.7.13: Do Exercise 12 assuming the container has a lid that is made from t...
 4.7.14: (a) Show that of all the rectangles with a given area, the one with...
 4.7.15: Find the point on the line that is closest to the origin.
 4.7.16: Find the point on the line that is closest to the point 3, 16x
 4.7.17: Find the points on the ellipse that are farthest away from the poin...
 4.7.18: Find, correct to two decimal places, the coordinates of the point o...
 4.7.19: Find the dimensions of the rectangle of largest area that can be in...
 4.7.20: Find the area of the largest rectangle that can be inscribed in the...
 4.7.21: Find the dimensions of the rectangle of largest area that can be in...
 4.7.22: Find the dimensions of the rectangle of largest area that has its b...
 4.7.23: Find the dimensions of the isosceles triangle of largest area that ...
 4.7.24: Find the area of the largest rectangle that can be inscribed in a r...
 4.7.25: A right circular cylinder is inscribed in a sphere of radius r. Fin...
 4.7.26: A right circular cylinder is inscribed in a cone with height h and ...
 4.7.27: A right circular cylinder is inscribed in a sphere of radius r. Fin...
 4.7.28: A Norman window has the shape of a rectangle surmounted by a semici...
 4.7.29: The top and bottom margins of a poster are each 6 cm and the side m...
 4.7.30: A poster is to have an area of 180 in with 1inch margins at the bo...
 4.7.31: A piece of wire 10 m long is cut into two pieces. One piece is bent...
 4.7.32: Answer Exercise 31 if one piece is bent into a square and the S oth...
 4.7.33: A cylindrical can without a top is made to contain of liquid. Find ...
 4.7.34: A fence 8 ft tall runs parallel to a tall building at a distance of...
 4.7.35: A coneshaped drinking cup is made from a circular piece of paper o...
 4.7.36: A coneshaped paper drinking cup is to be made to hold of water. Fi...
 4.7.37: A cone with height is inscribed in a larger cone with height so tha...
 4.7.38: For a fish swimming at a speed relative to the water, the energy ex...
 4.7.39: In a beehive, each cell is a regular hexagonal prism, open at one e...
 4.7.40: A boat leaves a dock at 2:00 P.M. and travels due south at a speed ...
 4.7.41: Solve the problem in Example 4 if the river is 5 km wide and point ...
 4.7.42: A woman at a point on the shore of a circular lake with radius 2 mi...
 4.7.43: The illumination of an object by a light source is directly proport...
 4.7.44: Find an equation of the line through the point that cuts off the le...
 4.7.45: Let and be positive numbers. Find the length of the shortest line s...
 4.7.46: At which points on the curve does the tangent line have the largest...
 4.7.47: Show that of all the isosceles triangles with a given perimeter, th...
 4.7.48: The frame for a kite is to be made from six pieces of wood. The fou...
 4.7.49: A point needs to be located somewhere on the line so that the total...
 4.7.50: The graph shows the fuel consumption of a car (measured in gallons ...
 4.7.51: Let be the velocity of light in air and the velocity of light in wa...
 4.7.52: Two vertical poles and are secured by a rope going from the top of ...
 4.7.53: The upper righthand corner of a piece of paper, 12 in. by 8 in., a...
 4.7.54: A steel pipe is being carried down a hallway 9 ft wide. At the end ...
 4.7.55: An observer stands at a point , one unit away from a track. Two run...
 4.7.56: A rain gutter is to be constructed from a metal sheet of width 30 c...
 4.7.57: Where should the point be chosen on the line segment so as to maxim...
 4.7.58: A painting in an art gallery has height and is hung so that its low...
 4.7.59: Find the maximum area of a rectangle that can be circumscribed abou...
 4.7.60: The blood vascular system consists of blood vessels (arteries, arte...
 4.7.61: Ornithologists have determined that some species of birds tend to a...
 4.7.62: Two light sources of identical strength are placed 10 m apart. An o...
Solutions for Chapter 4.7: Optimization Problems
Full solutions for Calculus,  5th Edition
ISBN: 9780534393397
Solutions for Chapter 4.7: Optimization Problems
Get Full SolutionsSince 62 problems in chapter 4.7: Optimization Problems have been answered, more than 43666 students have viewed full stepbystep solutions from this chapter. Chapter 4.7: Optimization Problems includes 62 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus,, edition: 5. Calculus, was written by and is associated to the ISBN: 9780534393397. This expansive textbook survival guide covers the following chapters and their solutions.

Aphelion
The farthest point from the Sun in a planetâ€™s orbit

Combinations of n objects taken r at a time
There are nCr = n! r!1n  r2! such combinations,

Complex plane
A coordinate plane used to represent the complex numbers. The xaxis of the complex plane is called the real axis and the yaxis is the imaginary axis

Constant of variation
See Power function.

Doubleangle identity
An identity involving a trigonometric function of 2u

Extracting square roots
A method for solving equations in the form x 2 = k.

Extraneous solution
Any solution of the resulting equation that is not a solution of the original equation.

Inverse cotangent function
The function y = cot1 x

Negative association
A relationship between two variables in which higher values of one variable are generally associated with lower values of the other variable.

nth root of unity
A complex number v such that vn = 1

Onetoone rule of exponents
x = y if and only if bx = by.

Positive numbers
Real numbers shown to the right of the origin on a number line.

Projectile motion
The movement of an object that is subject only to the force of gravity

Pseudorandom numbers
Computergenerated numbers that can be used to approximate true randomness in scientific studies. Since they depend on iterative computer algorithms, they are not truly random

Solve a triangle
To find one or more unknown sides or angles of a triangle

Solve by substitution
Method for solving systems of linear equations.

Statistic
A number that measures a quantitative variable for a sample from a population.

Symmetric about the origin
A graph in which (x, y) is on the the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ? + ?) is on the graph whenever (r, ?) is

Terminal point
See Arrow.

Time plot
A line graph in which time is measured on the horizontal axis.