 4.6.1: Consider the following problem: Find two numbers whose sum is 23 an...
 4.6.2: Find two numbers whose difference is 100 and whose product is a min...
 4.6.3: Find two positive numbers whose product is 100 and whose sum is a m...
 4.6.4: The sum of two positive numbers is 16. What is the smallest possibl...
 4.6.5: Find the dimensions of a rectangle with perimeter 100 m whose area ...
 4.6.6: Find the dimensions of a rectangle with area whose perimeter is as ...
 4.6.7: A model used for the yield of an agricultural crop as a function of...
 4.6.8: The rate at which photosynthesis takes place for a species of phyto...
 4.6.9: Consider the following problem: A farmer with 750 ft of fencing wan...
 4.6.10: Consider the following problem: A box with an open top is to be con...
 4.6.11: If 1200 cm of material is available to make a box with a square bas...
 4.6.12: A box with a square base and open top must have a volume of 32,000 ...
 4.6.13: (a) Show that of all the rectangles with a given area, the one with...
 4.6.14: A rectangular storage container with an open top is to have a volum...
 4.6.15: Find the points on the ellipse that are farthest away from the poin...
 4.6.16: Find, correct to two decimal places, the coordinates of the point o...
 4.6.17: Find the dimensions of the rectangle of largest area that can be in...
 4.6.18: Find the dimensions of the rectangle of largest area that has its b...
 4.6.19: A right circular cylinder is inscribed in a sphere of radius . Find...
 4.6.20: Find the area of the largest rectangle that can be inscribed in the...
 4.6.21: Find the dimensions of the isosceles triangle of largest area that ...
 4.6.22: A cylindrical can without a top is made to contain of liquid. Find ...
 4.6.23: A Norman window has the shape of a rectangle surmounted by a semici...
 4.6.24: A right circular cylinder is inscribed in a cone with height and ba...
 4.6.25: A piece of wire 10 m long is cut into two pieces. One piece is bent...
 4.6.26: A fence 8 ft tall runs parallel to a tall building at a distance of...
 4.6.27: A coneshaped drinking cup is made from a circular piece of paper o...
 4.6.28: A coneshaped paper drinking cup is to be made to hold of water. Fi...
 4.6.29: A cone with height is inscribed in a larger cone with height so tha...
 4.6.30: The graph shows the fuel consumption of a car (measured in gallons ...
 4.6.31: If a resistor of ohms is connected across a battery of volts with i...
 4.6.32: For a sh swimming at a speed relative to the water, the energy expe...
 4.6.33: In a beehive, each cell is a regular hexagonal prism, open at one e...
 4.6.34: A boat leaves a dock at 2:00 PM and travels due south at a speed of...
 4.6.35: An oil renery is located on the north bank of a straight river that...
 4.6.36: Suppose the renery in Exercise 35 is located 1 km north of the rive...
 4.6.37: The illumination of an object by a light source is directly proport...
 4.6.38: A woman at a point on the shore of a circular lake with radius 2 mi...
 4.6.39: Find an equation of the line through the point that cuts off the le...
 4.6.40: At which points on the curve does the tangent line have the largest...
 4.6.41: What is the shortest possible length of the line segment that is cu...
 4.6.42: What is the smallest possible area of the triangle that is cut off ...
 4.6.43: (a) If is the cost of producing units of a commodity, then the aver...
 4.6.44: (a) Show that if the prot is a maximum, then the marginal revenue e...
 4.6.45: A baseball team plays in a stadium that holds 55,000 spectators. Wi...
 4.6.46: During the summer months Terry makes and sells necklaces on the bea...
 4.6.47: A manufacturer has been selling 1000 television sets a week at each...
 4.6.48: The manager of a 100unit apartment complex knows from experience t...
 4.6.49: Let and be positive numbers. Find the length of the shortest line s...
 4.6.50: The frame for a kite is to be made from six pieces of wood. The fou...
 4.6.51: Let be the velocity of light in air and the velocity of light in wa...
 4.6.52: Two vertical poles and are secured by a rope going from the top of ...
 4.6.53: The upper righthand corner of a piece of paper, 12 in. by 8 in., a...
 4.6.54: A steel pipe is being carried down a hallway 9 ft wide. At the end ...
 4.6.55: Find the maximum area of a rectangle that can be circumscribed abou...
 4.6.56: A rain gutter is to be constructed from a metal sheet of width 30 c...
 4.6.57: Where should the point be chosen on the line segment so as to maxim...
 4.6.58: A painting in an art gallery has height and is hung so that its low...
 4.6.59: Ornithologists have determined that some species of birds tend to a...
 4.6.60: The blood vascular system consists of blood vessels (arteries, arte...
 4.6.61: The speeds of sound in an upper layer and in a lower layer of rock ...
 4.6.62: Two light sources of identical strength are placed 10 m apart. An o...
Solutions for Chapter 4.6: OPTIMIZATION PROBLEMS
Full solutions for Single Variable Calculus: Concepts and Contexts (Stewart's Calculus Series)  4th Edition
ISBN: 9780495559726
Solutions for Chapter 4.6: OPTIMIZATION PROBLEMS
Get Full SolutionsSingle Variable Calculus: Concepts and Contexts (Stewart's Calculus Series) was written by and is associated to the ISBN: 9780495559726. Chapter 4.6: OPTIMIZATION PROBLEMS includes 62 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Single Variable Calculus: Concepts and Contexts (Stewart's Calculus Series), edition: 4. Since 62 problems in chapter 4.6: OPTIMIZATION PROBLEMS have been answered, more than 9752 students have viewed full stepbystep solutions from this chapter.

Direction angle of a vector
The angle that the vector makes with the positive xaxis

Elimination method
A method of solving a system of linear equations

Halflife
The amount of time required for half of a radioactive substance to decay.

Inverse properties
a + 1a2 = 0, a # 1a

Matrix, m x n
A rectangular array of m rows and n columns of real numbers

Minor axis
The perpendicular bisector of the major axis of an ellipse with endpoints on the ellipse.

Negative linear correlation
See Linear correlation.

Piecewisedefined function
A function whose domain is divided into several parts with a different function rule applied to each part, p. 104.

Polynomial function
A function in which ƒ(x)is a polynomial in x, p. 158.

Random numbers
Numbers that can be used by researchers to simulate randomness in scientific studies (they are usually obtained from lengthy tables of decimal digits that have been generated by verifiably random natural phenomena).

Rational function
Function of the form ƒ(x)/g(x) where ƒ(x) and g(x) are polynomials and g(x) is not the zero polynomial.

Rigid transformation
A transformation that leaves the basic shape of a graph unchanged.

Root of an equation
A solution.

Sample standard deviation
The standard deviation computed using only a sample of the entire population.

Scalar
A real number.

Solve an equation or inequality
To find all solutions of the equation or inequality

Solve by substitution
Method for solving systems of linear equations.

Sphere
A set of points in Cartesian space equally distant from a fixed point called the center.

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

Wrapping function
The function that associates points on the unit circle with points on the real number line