Planning a Diet Pauls diet is to contain at least 24 units

In Exercises 14, find the x- and y-intercepts of the line and draw its graph.2x - 3y = 6

In Exercises 14, find the x- and y-intercepts of the line and draw its graph.5x + 10y = 30

In Exercises 14, find the x- and y-intercepts of the line and draw its graph.x 20 + y 50 = 1

In Exercises 14, find the x- and y-intercepts of the line and draw its graph.x 30 - y 20 = 1

In Exercises 59, find the point of intersection of the two lines. (We will use these values in Examples 7 and 8.)4x + y = 180 and x + y = 90

In Exercises 59, find the point of intersection of the two lines. (We will use these values in Examples 7 and 8.)x + y = 90 10x + 5y = 800

In Exercises 59, find the point of intersection of the two lines. (We will use these values in Examples 7 and 8.)4x + y = 180 10x + 5y = 800

In Exercises 59, find the point of intersection of the two lines. (We will use these values in Examples 7 and 8.)8x + 2y = 24 x + y = 6

In Exercises 59, find the point of intersection of the two lines. (We will use these values in Examples 7 and 8.)x + y = 6 2x + 8y = 30

In Exercises 59, find the point of intersection of the two lines. (We will use these values in Examples 7 and 8.)Solve the system of equations: 2x + 3y = 4 y = x 2

In Exercises 16, match the inequality with its graph. Indicate whether the boundary is included in or excluded from the graph. All graphs are drawn in by x 3

In Exercises 16, match the inequality with its graph. Indicate whether the boundary is included in or excluded from the graph. All graphs are drawn in by y 7 2

In Exercises 16, match the inequality with its graph. Indicate whether the boundary is included in or excluded from the graph. All graphs are drawn in by 2x - 5y 2

In Exercises 16, match the inequality with its graph. Indicate whether the boundary is included in or excluded from the graph. All graphs are drawn in by y 7 11/22x 2-1

In Exercises 16, match the inequality with its graph. Indicate whether the boundary is included in or excluded from the graph. All graphs are drawn in by y 2 - x2

In Exercises 16, match the inequality with its graph. Indicate whether the boundary is included in or excluded from the graph. All graphs are drawn in by x 2 + y26 4

In Exercises 716, draw a hand sketch of the inequality. State the boundary of the region.x 4

In Exercises 716, draw a hand sketch of the inequality. State the boundary of the region.y -3

In Exercises 716, draw a hand sketch of the inequality. State the boundary of the region.2x + 5y 7

In Exercises 716, draw a hand sketch of the inequality. State the boundary of the region.3x - y 7 4

In Exercises 716, draw a hand sketch of the inequality. State the boundary of the region.y 6 x - 2 + 1

In Exercises 716, draw a hand sketch of the inequality. State the boundary of the region.y x2-3

In Exercises 716, draw a hand sketch of the inequality. State the boundary of the region.x 2 + y2 6 9

In Exercises 716, draw a hand sketch of the inequality. State the boundary of the region.x 2 + y2 4

In Exercises 716, draw a hand sketch of the inequality. State the boundary of the region.y 7 2x

In Exercises 716, draw a hand sketch of the inequality. State the boundary of the region.y 6 sin x

Use an algebraic method in Exercises 1722 to solve the system of inequalities. Support with a grapher.3x + 4y 18 5x - 3y 7 1

Use an algebraic method in Exercises 1722 to solve the system of inequalities. Support with a grapher.2x - y -8 4x + 3y -6

Use an algebraic method in Exercises 1722 to solve the system of inequalities. Support with a grapher.y x 2 - 2 y 2x + 3

Use an algebraic method in Exercises 1722 to solve the system of inequalities. Support with a grapher.y 7 -x 2 - 2x + 2 x - 3y - 6 6 0

Use an algebraic method in Exercises 1722 to solve the system of inequalities. Support with a grapher.x 2 + y2 4 y x 2

Use an algebraic method in Exercises 1722 to solve the system of inequalities. Support with a grapher.y x x 2 + y2 9

Use an algebraic method in Exercises 2326 to solve the system of inequalities. Support with a grapher. In Exercises 2326, solve the system of inequalities.y 0 x 0 x + 2y 80 2x + y 80

Use an algebraic method in Exercises 2326 to solve the system of inequalities. Support with a grapher. In Exercises 2326, solve the system of inequalities.y 0 x 6 9x + 4y 360 3x + 8y 240

Use an algebraic method in Exercises 2326 to solve the system of inequalities. Support with a grapher. In Exercises 2326, solve the system of inequalities.y 0 x 0 x + y 2 2x + 3y 18 5x + 2y 20

Use an algebraic method in Exercises 2326 to solve the system of inequalities. Support with a grapher. In Exercises 2326, solve the system of inequalities.x + y 30 3x + 7y 210 7x + 3y 210

In Exercises 2730, write a system of inequalities whose solution is the region shaded in the given figure. All boundaries are to be included.

In Exercises 2730, write a system of inequalities whose solution is the region shaded in the given figure. All boundaries are to be included.

In Exercises 2730, write a system of inequalities whose solution is the region shaded in the given figure. All boundaries are to be included.

In Exercises 2730, write a system of inequalities whose solution is the region shaded in the given figure. All boundaries are to be included.

Objective function: Constraints:x 0, y 0 x - 2y 0 x + y 80 = 4x + 3y

Objective function: Constraints:x 0, y 0 3x - y 0 x + y 90 = 10x + 11y

Objective function: Constraints:x 0 y 0 4x + 6y 204 x + 6y 60 5x + y 60 = 7x + 4y

Objective function: Constraints:x 0, y 0 11x + 28y 380 x + 8y 40 3x + 4y 60 f = 15x + 25y

Objective function: Constraints:x 0 y 0 x + 2y 10 4x + 3y 30 2x + y 12 = 5x + 2y

Objective function: Constraints:x 0 y 0 2x + 7y 30 5x + 6y 52 3x + 2y 20 = 3x + 5y

Mining Ore Pearsons Metals mines two ores: R and S. The company extracts minerals A and B from each type of ore. It costs $50 per ton to extract 80 lb of A and 160 lb of B from ore R. It costs $60 per ton to extract 140 lb of A and 50 lb of B from ore S. Pearsons must produce at least 4000 lb of A and 3200 lb of B. How much of each ore should be processed to minimize cost? What is the minimum cost?

Planning a Diet Pauls diet is to contain at least 24 units of carbohydrates and 16 units of protein. Food substance A costs $1.40 per unit and each unit contains 3 units of carbohydrates and 4 units of protein. Food substance B costs $0.90 per unit and each unit contains 2 units of carbohydrates and 1 unit of protein. How many units of each food substance should be purchased in order to minimize cost? What is the minimum cost?

Producing Gasoline Two oil refineries produce three grades of gasoline: A, B, and C. At each refinery, the three grades of gasoline are produced in a single operation in the following proportions: Refinery 1 produces 1 unit of A, 2 units of B, and 1 unit of C; Refinery 2 produces 1 unit of A, 4 units of B, and 4 units of C. For the production of one operation, Refinery 1 charges $300 and Refinery 2 charges $600. A customer needs 100 units of A, 320 units of B, and 200 units of C. How should the orders be placed if the customer is to minimize his cost?

Maximizing Profit A manufacturer wants to maximize the profit for two products. Product A yields a profit of $2.25 per unit, and product B yields a profit of $2.00 per unit. Demand information requires that the total number of units produced be no more than 3000 units, and that the number of units of product B produced be greater than or equal to half the number of units of product A produced. How many of each unit should be produced to maximize profit?

True or False The graph of a linear inequality in x and y is a half-line. Justify your answer.

True or False The boundary of the solution of is the graph of Justify your answer.

For Exercises 4344, use the figure below, which shows the graphs of the two lines 3x + 4y = 5 and 2x - 3y = 4.Which of the following represents the solution of the system (A) Region I plus its boundary (B) Region I without its boundary (C) Region II plus its boundary (D) Region II without its boundary (E) Region IV plus its boundary

For Exercises 4344, use the figure below, which shows the graphs of the two lines 3x + 4y = 5 and 2x - 3y = 4.Which of the following represents the solution of the system (A) Region II plus its boundary (B) Region III plus its boundary (C) Region III without its boundary (D) Region IV plus its boundary (E) Region IV without its boundary

Exercises 4546 refer to the following linear programming problem: Objective function: Constraints:x 0, y 0 x + 3y 12 2x + y 10 = 5x + 10y Which of the following is not a corner point? (A) 0, 0 (B) 5, 0 (C) 0, 4 (D) 3, 4 (E)

Exercises 4546 refer to the following linear programming problem: Objective function: Constraints:x 0, y 0 x + 3y 12 2x + y 10 = 5x + 10y What is the maximum value of in the feasible region of the problem? (A) 0 (B) 25 (C) 40 (D) 46 (E) 55

Revisiting Example 6 Consider the objective function of Example 6. (a) Prove that for any two real number values for f, the two lines are parallel. (b) Writing to Learn For give reasons why the line moves farther away from the origin as the value of increases. (c) Writing to Learn Give a geometric explanation of why the region of Example 6 must contain a minimum and a maximum value for .

Writing to Learn Describe all the possible ways that two distinct parabolas of the form can intersect. Give examples.

Implicit Functions The equation defines y as two implicit functions of x. Solve for y to find the two functions and draw the graph of the equation.

Implicit Functions The equation defines y as two implicit functions of x. Solve for y to find the two functions and draw the graph of the equation.

Solve the system of inequalities: [Hint: See Exercise 49.]

Graph the inequality x [Hint: See Exercise 50.]