Explanation Given: A package of gardening and potting mixture requires 2 lb of the soil and 1 lb of soil respectively. A package of gardening and potting mixture requires 1 lb of peat moss and 2 lb of peat moss respectively. A package of gardening and potting mixture requires 1 lb of fertilizer and 3 lb of fertilizer respectively. Karla’s has at most 16 lb of soil and 11 lb of peat moss and 15 lb of fertilizer. The total cost of gardening mixture is $3 and potting mixture is $5. Calculation: Let x represents the number of packages of gardening mixture and y represents the number of packages of potting mixture. From the given data, the following observations are made. Maximize z = 3 x + 5 y . Subject to: 2 x + y ≤ 16 (1) x + 2 y ≤ 11 (2) x + 3 y ≤ 15 (3) Consider the equation (1). The given inequality in the equation is ≤ . Therefore, the solid line is used to join the coordinates of this equation. Now, replace the inequality symbol in the given equation (1) with an “equals” sign. Then the equation (1) becomes, 2 x + y = 16 . Obtain any 2 coordinates of the above equation to plot on the line. Consider x = 0 , 8 and obtain corresponding values of y respectively. Substitute x = 0 in the linear equation 2 x + y = 16 . 2 ( 0 ) + y = 16 y = 16 Thus, the value of y is 16 at x = 0 . Hence, the coordinate of first point is ( 0 , 16 ) . Substitute x = 8 in the linear equation 2 x + y = 16 . 2 ( 8 ) + y = 16 16 + y = 16 y = 16 − 16 y = 0 Thus, the value of y is 0 at x = 8 . Hence, the coordinate of second point is ( 8 , 0 ) . The coordinates are ( 0 , 16 ) and ( 8 , 0 ) . Use the test point to determine the half plane which is to be shaded. Let the test point be ( 0 , 0 ) . Now substitute the test point ( 0 , 0 ) in 2 x + y ≤ 16 . 2 ( 0 ) + 0 ≤ 16 0 ≤ 16 It is noticed that the inequality 2 x + y ≤ 16 is true. Thus, shade the half-plane that contain the test point ( 0 , 0 ) . That is, the half plane below the line. Consider the equation (2). The given inequality in the equation is ≤ . Therefore, the solid line is used to join the coordinates of this equation. Now, replace the inequality symbol in the given equation (2) with an “equals” sign. Then the equation becomes, x + 2 y = 11 . Obtain any 2 coordinates of the above equation to plot on the line. Consider x = 0 , 11 and obtain corresponding values of y respectively. Substitute x = 0 in the linear equation x + 2 y = 11 . 0 + 2 y = 11 2 y = 11 y = 11 2 Thus, the value of y is 11 2 at x = 0 . Hence, the coordinate of first point is ( 0 , 11 2 ) . Substitute x = 11 in the linear equation x + 2 y = 11 . 11 + 2 y = 11 2 y = 11 − 11 y = 0 Hence, the coordinate of second point is ( 11 , 0 ) . The coordinates are ( 0 , 11 2 ) and ( 11 , 0 ) . Use the test point to determine the half plane which is to be shaded. Let the test point be ( 0 , 0 ) . Now substitute the test point ( 0 , 0 ) in x + 2 y ≤ 11 . 0 + 2 ( 0 ) ≤ 11 0 ≤ 11 It is noticed that the inequality x + 2 y ≤ 11 is true. Thus, shade the half-plane that contain the test point ( 0 , 0 ) . That is, the half plane below the line. Consider the equation (3)

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Chapter 3, Problem 41RE

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Chapter 3, Problem 40RE

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Chapter 3 Solutions

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Ch. 3.1 - Graph 3x + 2y 18.Ch. 3.1 - Graph the feasible region for the system...Ch. 3.1 - Prob. 1WE Ch. 3.1 - y=12x+1 Ch. 3.1 - Prob. 3WE Ch. 3.1 - Prob. 4WE Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E

Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Graph the feasible region for each system of...Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Graph the feasible region for each system of...Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - The regions A through G in the figure can be...Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - For Exercises 4247, perform the following steps....Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - For Exercises 4247, perform the following steps....Ch. 3.1 - Prob. 47E Ch. 3.2 - Prob. 1YT Ch. 3.2 - Prob. 1WE Ch. 3.2 - Prob. 2WE Ch. 3.2 - Prob. 3WE Ch. 3.2 - Prob. 4WE Ch. 3.2 - Prob. 1E Ch. 3.2 - Prob. 2E Ch. 3.2 - Prob. 3E Ch. 3.2 - Prob. 4E Ch. 3.2 - Prob. 5E Ch. 3.2 - Prob. 6E Ch. 3.2 - Prob. 7E Ch. 3.2 - Prob. 8E Ch. 3.2 - Prob. 9E Ch. 3.2 - Prob. 10E Ch. 3.2 - Prob. 11E Ch. 3.2 - Prob. 12E Ch. 3.2 - Prob. 13E Ch. 3.2 - Prob. 14E Ch. 3.2 - Prob. 15E Ch. 3.2 - Prob. 16E Ch. 3.2 - Prob. 17E Ch. 3.3 - Prob. 1YT Ch. 3.3 - Prob. 2YT Ch. 3.3 - Prob. 3YT Ch. 3.3 - Prob. 1WE Ch. 3.3 - Prob. 2WE Ch. 3.3 - Prob. 1E Ch. 3.3 - Prob. 2E Ch. 3.3 - Prob. 3E Ch. 3.3 - Prob. 4E Ch. 3.3 - Prob. 5E Ch. 3.3 - Prob. 6E Ch. 3.3 - Prob. 7E Ch. 3.3 - Prob. 8E Ch. 3.3 - Finance A pension fund manager decides to invest a...Ch. 3.3 - Prob. 10E Ch. 3.3 - Prob. 11E Ch. 3.3 - Prob. 12E Ch. 3.3 - Blending The Mostpure Milk Company gets milk from...Ch. 3.3 - Profit The Muro Manufacturing Company makes two...Ch. 3.3 - Revenue A machine shop manufactures two types of...Ch. 3.3 - Revenue The manufacturing process requires that...Ch. 3.3 - Transportation A flash drive manufacturer has 370...Ch. 3.3 - Prob. 18E Ch. 3.3 - Prob. 19E Ch. 3.3 - Prob. 20E Ch. 3.3 - Life Sciences 21. Health Care David Willis takes...Ch. 3.3 - Predator Food Requirements A certain predator...Ch. 3.3 - Nutrition A dietician is planning a snack package...Ch. 3.3 - Health Care Jennifer Morales was given the...Ch. 3.3 - Prob. 25E Ch. 3.3 - Prob. 26E Ch. 3 - Determine whether each of the following statements...Ch. 3 - Determine whether each of the following statements...Ch. 3 - Determine whether each of the following statements...Ch. 3 - Prob. 4RE Ch. 3 - Determine whether each of the following statements...Ch. 3 - Prob. 6RE Ch. 3 - Determine whether each of the following statements...Ch. 3 - Prob. 8RE Ch. 3 - Determine whether each of the following statements...Ch. 3 - Prob. 10RE Ch. 3 - Determine whether each of the following statements...Ch. 3 - Prob. 12RE Ch. 3 - Determine whether each of the following statements...Ch. 3 - Prob. 14RE Ch. 3 - Graph each linear inequality. 15. y 2x + 3 Ch. 3 - Prob. 16RE Ch. 3 - Graph each linear inequality. 17. 2x + 6y 8 Ch. 3 - Prob. 18RE Ch. 3 - Graph each linear inequality. 19. y x Ch. 3 - Prob. 20RE Ch. 3 - Graph the solution of each system of inequalities....Ch. 3 - Prob. 22RE Ch. 3 - Graph the solution of each system of inequalities....Ch. 3 - Prob. 24RE Ch. 3 - Graph the solution of each system of inequalities....Ch. 3 - Prob. 26RE Ch. 3 - Use the given regions to find the maximum and...Ch. 3 - Prob. 28RE Ch. 3 - Use the graphical method to solve each linear...Ch. 3 - Prob. 30RE Ch. 3 - Use the graphical method to solve each linear...Ch. 3 - Prob. 32RE Ch. 3 - Prob. 33RE Ch. 3 - Prob. 34RE Ch. 3 - It is not necessary to check all corner points in...Ch. 3 - Prob. 36RE Ch. 3 - Prob. 37RE Ch. 3 - Prob. 38RE Ch. 3 - Profit Refer to Exercise 37. (a) How many batches...Ch. 3 - Prob. 40RE Ch. 3 - Prob. 41RE Ch. 3 - Construction A contractor builds boathouses in two...Ch. 3 - Prob. 43RE Ch. 3 - Prob. 44RE Ch. 3 - Prob. 45RE Ch. 3 - General Interest 46. Studying Ty Olden is trying...

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The number of gardening mixture and potting mixture should she make in order to maximize income.

Solution Summary: The author explains how the maximum income of 31 can be achieved by preparing 7 packages of gardening and potting mixture. The solid line is used to join the coordinates of the equation.

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