SPORTS St Andrews Golf Course in St Andrews, Scotland is

x y  2 x y  0

2x x 3y y   3 0

4x 8x y y 1 17   0 0

10x x 6y 9y 14 7   0 0

0.5x 1.25x y 4.5y   0.75 2.5

x x 2 5y 1 5y   3 5 4 5

x2 y2  9 x y  1

x2 y2  169 3x 2y  39

y  2x2 y  x 4 2x2

x  y 3 x  y2 1

2x y  x 5y  10 6

8x 2x 3y 5y   3 28

y  y  2x2 4x 1 x2 4x 3

y2 2y x  0 x y  0

2ex y  y  2ex 0

x2 2x y2 3y   100 12 2

y  2 log x y  3 4x 5

y  y  ln x 1 3 4 1 2 x

BREAK-EVEN ANALYSIS You set up a scrapbook business and make an initial investment of $50,000. The unit cost of a scrapbook kit is $12 and the selling price is $25. How many kits must you sell to break even?

CHOICE OF TWO JOBS You are offered two sales jobs at a pharmaceutical company. One company offers an annual salary of $55,000 plus a year-end bonus of 1.5% of your total sales. The other company offers an annual salary of $52,000 plus a year-end bonus of 2% of your total sales. What amount of sales will make the second offer better? Explain

GEOMETRY The perimeter of a rectangle is 480 meters and its length is 150% of its width. Find the dimensions of the rectangle.

GEOMETRY The perimeter of a rectangle is 68 feet and its width is times its length. Find the dimensions of the rectangle.

GEOMETRY The perimeter of a rectangle is 40 inches. The area of the rectangle is 96 square inches. Find the dimensions of the rectangle.

BODY MASS INDEX Body Mass Index (BMI) is a measure of body fat based on height and weight. The 75th percentile BMI for females, ages 9 to 20, is growing more slowly than that for males of the same age range. Models that represent the 75th percentile BMI for males and females, ages 9 to 20, are given by Males Females where is the BMI and represents the age, with corresponding to 9 years of age. Use a graphing utility to determine whether the BMI for males ever exceeds the BMI for females.

2x y  2 6x 8y  39 9

40x 30y  20x 50y  24 14

0.2x 0.3y  0.14 0.4x 0.5y  0.20

12x 42y  30x 18y  17 19

3x 2y  0 3x 2 y 5  10

7x 12y  63 2x 3 y 2  21

1.25x 5x 2y  8y  3.5 14

1.5x 6x 2.5y 10y   8.5 24

x 5y  4 x 3y  6

3x y  7 9x 3y  21

3x y  7 6x 2y  8

2x y  3 x 5y  4

p  37 0.0002x p

p  120 0.0001x p  45 0.0002x

x 4y 3z  y z  z  3 1 5 9.3

x 7y 8z  y 9z  z  85 35 3

4x 3y 8y 2z 7z z    65 14 10  x

5x 3y 7z 8z z    9 4 7  4

x 3x 4x 2y 2y 6z  z  2z  4 4 16

x 2x 4x 3y y z  13 5z  23 2z  14  x

x 2y 2x 3y x 3y z 3z    6 7 11  x

2x 3x 3x 2y y 6z  9 11z  16 7z  11  x

x 4x 3y 2y y z 2z 4w w 3w     1 4 2 5

x 3x 2x x y 4y 3y 4y z z z w w 3w 2w     6 3 6 7

5x 12y 7z  16 3x 7y 4z  9

2x 5y 19z  34 3x 8y 31z  54

4 4 4 (1, 2) (0, 5) (2, 5) y

1, 0) (5, 6) 12 6 6 12 24 x y

1 4 32 1 5 (2, 1) (5, 2) (1, 2) x y

) 6 2 24 2 8 x y

DATA ANALYSIS: ONLINE SHOPPING The table shows the projected online retail sales (in billions of dollars) in the United States from 2010 through 2012. (Source: Forrester Research, Inc.) (a) Use the technique demonstrated in Exercises 7780 in Section 9.3 to set up a system of equations for the data and to find a least squares regression parabola that models the data. Let represent the year, with corresponding to 2010. (b) Use a graphing utility to graph the parabola and the data in the same viewing window. How well does the model fit the data? (c) Use the model to estimate the online retail sales in the United States in 2015. Does your answer seem reasonable?

AGRICULTURE A mixture of 6 gallons of chemical A, 8 gallons of chemical B, and 13 gallons of chemical C is required to kill a destructive crop insect. Commercial spray X contains 1, 2, and 2 parts, respectively, of these chemicals. Commercial spray Y contains only chemical C. Commercial spray Z contains chemicals A, B, and C in equal amounts. How much of each type of commercial spray is needed to get the desired mixture?

INVESTMENT ANALYSIS An inheritance of $40,000 was divided among three investments yielding $3500 in interest per year. The interest rates for the three investments were 7%, 9%, and 11%. Find the amount placed in each investment if the second and third were $3000 and $5000 less than the first, respectively

VERTICAL MOTION An object moving vertically is at the given heights at the specified times. Find the position equation for the object. (a) At second, feet At seconds, feet At seconds, feet (b) At second, feet At seconds, feet At seconds, feet

SPORTS Pebble Beach Golf Links in Pebble Beach, California is an 18-hole course that consists of par-3 holes, par-4 holes, and par-5 holes. There are two more par-4 holes than twice the number of par-5 holes, and the number of par-3 holes is equal to the number of par-5 holes. Find the numbers of par-3, par-4, and par-5 holes on the course.

SPORTS St Andrews Golf Course in St Andrews, Scotland is one of the oldest golf courses in the world. It is an 18-hole course that consists of par-3 holes, par-4 holes, and par-5 holes. There are seven times as many par-4 holes as par-5 holes, and the sum of the numbers of par-3 and par-5 holes is four. Find the numbers of par-3, par-4, and par-5 holes on the course.

3 x2 20x

x 8 x2 3x 28 3

3x 4 x3 5x2 x

x 2 x x2 22

4 x x2 6x 8

x x2 3x 2

x2 x2 2x 15

9 x2 9

x2 2x x3 x2 x 1 9

4x 3 x 12

3x2 4x x2 12

4x2 x 1 x2 1

y  5 3y x  7 1 2 x 9

3y x  7 1

y 4x2 > 1 y

y  3 x2 2

x 12 y 32 < 16 y

x2 y 52 > 1

x 3x 2y  160 y  180 x  0 y  0

2x 3y  24 2x y  16 x  0 y  0

3x 2y  24 x 2y  12 2  x  15 y  15

2x y  16 x 3y  18 0  x  25 0  y  25

y < x 1 y > x2 1

y  6 2x x2 y  x 6

2x 3y  0 2x y  8 y  0

x2 y2  9 x 32 y2  9

INVENTORY COSTS A warehouse operator has 24,000 square feet of floor space in which to store two products. Each unit of product I requires 20 square feet of floor space and costs $12 per day to store. Each unit of product II requires 30 square feet of floor space and costs $8 per day to store. The total storage cost per day cannot exceed $12,400. Find and graph a system of inequalities describing all possible inventory levels.

NUTRITION A dietitian is asked to design a special dietary supplement using two different foods. Each ounce of food X contains 12 units of calcium, 10 units of iron, and 20 units of vitamin B. Each ounce of food Y contains 15 units of calcium, 20 units of iron, and 12 units of vitamin B. The minimum daily requirements of the diet are 300 units of calcium, 280 units of iron, and 300 units of vitamin B. (a) Write a system of inequalities describing the different amounts of food X and food Y that can be used. (b) Sketch a graph of the region in part (a). (c) Find two solutions to the system and interpret their meanings in the context of the problem.

p  160 0.0001x p  70 0.0002x

p  130 0.0002x p  30 0.0003x

GEOMETRY Derive a set of inequalities to describe the region of a rectangle with vertices at and

DATA ANALYSIS: COMPUTER SALES The table shows the sales (in billions of dollars) for Dell, Inc. from 2000 through 2007.

Objective function:

Objective function: Constraints: Constraints:

Objective function

Objective function:

Objective function:

Objective function:

OPTIMAL REVENUE A student is working part time as a hairdresser to pay college expenses. The student may work no more than 24 hours per week. Haircuts cost $25 and require an average of 20 minutes, and permanents cost $70 and require an average of 1 hour and 10 minutes. What combination of haircuts and/or permanents will yield an optimal revenue? What is the optimal revenue?

OPTIMAL PROFIT A shoe manufacturer produces a walking shoe and a running shoe yielding profits of $18 and $24, respectively. Each shoe must go through three processes, for which the required times per unit are shown in the table.

OPTIMAL PROFIT A manufacturer produces two models of bicycles. The times (in hours) required for assembling, painting, and packaging each model are shown in the table.

OPTIMAL COST A pet supply company mixes two brands of dry dog food. Brand X costs $15 per bag and contains eight units of nutritional element A, one unit of nutritional element B, and two units of nutritional element C. Brand Y costs $30 per bag and contains two units of nutritional element A, one unit of nutritional element B, and seven units of nutritional element C. Each bag of mixed dog food must contain at least 16 units, 5 units, and 20 units of nutritional elements A, B, and C, respectively. Find the numbers of bags of brands X and Y that should be mixed to produce a mixture meeting the minimum nutritional requirements and having an optimal cost. What is the optimal cost?

OPTIMAL COST Regular unleaded gasoline and premium unleaded gasoline have octane ratings of 87 and 93, respectively. For the week of March 23, 2009, regular unleaded gasoline in Houston, Texas averaged $1.85 per gallon. For the same week, premium unleaded gasoline averaged $2.10 per gallon. Determine the blend of regular and premium unleaded gasoline that results in an optimal cost of mid-grade unleaded (89-octane) gasoline. What is the optimal cost?

If a system of equations consists of a circle and a parabola, it is possible for the system to have three solutions.

The system represents the region covered by an isosceles trapezoid.

It is possible for an objective function of a linear programming problem to have exactly 10 maximum value points.

8, 10

5, 4

4 3, 2003

2, 11 5  4

4, 1, 2003

3, 5, 2006

5, 3 2, 2

1 2, 2, 3 4

WRITING Explain what is meant by an inconsistent system of linear equations.

How can you tell graphically that a system of linear equations in two variables has no solution? Give an example.