Explanation Let x and y represents the number of square feet of window space and wall space, respectively. In a small town in south Carolina, zoning rules require that the window space in a house be at least one-sixth of the space by solid walls. That is x ≥ 1 6 y . The cost to build windows and solid are $10 per ft 2 and $20 per ft 2 respectively and the total amount available for building walls and windows is no more than $12,000. That is, 10 x + 20 y ≤ 12 , 000 . The monthly estimated cost to heat the house is $10 for each square foot of windows and the $0.20 for each square foot of solid walls and available to pay for heat is no more than $160 per month. That is, 0.32 x + 0.20 y ≤ 160 From the above information, the linear programing problem can be stated as follows, Maximize z = x + y Subject to the constraints, x ≥ 1 6 y (1) 10 x + 20 y ≤ 12 , 000 (2) 0.32 x + 0.20 y ≤ 160 (3) x ≥ 0 y ≥ 0 Consider the equation (1). Rewrite the given equation, x − 1 6 y ≥ 0 . The given inequality in the equation is ≥ . Therefore, the solid line is used to join the coordinates of this equation. Now, replace the symbol ≥ by the symbol = in given equation (1). Then the equation (1) becomes, x − 1 6 y = 0 . Obtain any 2 coordinates of the above equation to plot on the line. Consider x = 0 and obtain the corresponding values of y respectively. Substitute x = 0 in the linear equation x − 1 6 y = 0 . 0 − 1 6 y = 0 − 1 6 y = 0 y = 0 Thus, the value of y is 0 at x = 0 . Hence, the first coordinate is ( 0 , 0 ) . Consider the point x = 1 , y = 6 . Substitute x = 1 , y = 6 in the linear equation x − 1 6 y = 0 . 1 − 1 6 ( 6 ) = 0 1 − 1 = 0 0 = 0 Hence, the second coordinate is ( 1 , 6 ) . Therefore, the coordinates are ( 0 , 0 ) and ( 1 , 6 ) . Use the test point to determine the half plane which is to be shaded. For x ≥ 1 6 y , the test point be ( 1 , 1 ) . Now substitute the test point ( 1 , 1 ) in x − 1 6 y ≥ 0 . 1 − 1 6 ( 1 ) ≥ 0 6 − 1 6 ≥ 0 5 6 ≥ 0 It is noticed that the inequality x − 1 6 y ≥ 0 is true. Thus, shade the half-plane that contain the test point ( 1 , 1 ) . 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 symbol ≤ by the symbol = in given equation (2). Then the equation (2) becomes, 10 x + 20 y = 12 , 000 . Obtain any 2 coordinates of the above equation to plot on the line. Consider x = 0 , 1200 and obtain the corresponding values of y respectively. Substitute x = 0 in the linear equation 10 x + 20 y = 12 , 000 . 10 ( 0 ) + 20 y = 12 , 000 20 y = 12 , 000 y = 12 , 000 20 y = 600 Thus, the value of y is 600 at x = 0 . Hence, the first coordinate is ( 0 , 600 ) . Substitute x = 1200 in the linear equation 10 x + 20 y = 12 , 000 . 10 ( 1200 ) + 20 y = 12 , 000 1200 + 20 y = 12000 20 y = 12000 − 12000 y = 0 Hence, the second coordinate is ( 1200 , 0 )

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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 maximum total area.

Solution Summary: The author explains that the maximum total area is 690.91 sq ft, and the cost to build windows and solid walls is 10 per square foot.

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