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 )

Finite Mathematics and Calculus with Applications (10th Edition)

10th Edition

ISBN: 9780321979407

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 3.3, Problem 26E

To determine

To find: The maximum total area.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3.3, Problem 25E

Chapter 3, Problem 1RE

Students have asked these similar questions

Rylee's car is stuck in the mud. Roman and Shanice come along in a truck to help pull her out. They attach one end of a tow strap to the front of the car and the other end to the truck's trailer hitch, and the truck starts to pull. Meanwhile, Roman and Shanice get behind the car and push. The truck generates a horizontal force of 377 lb on the car. Roman and Shanice are pushing at a slight upward angle and generate a force of 119 lb on the car. These forces can be represented by vectors, as shown in the figure below. The angle between these vectors is 20.2°. Find the resultant force (the vector sum), then give its magnitude and its direction angle from the positive x-axis. 119 lb 20.2° 377 lb

An airplane flies due west at an airspeed of 428 mph. The wind blows in the direction of 41° south of west at 50 mph. What is the ground speed of the airplane? What is the bearing of the airplane?

A vector with magnitude 5 points in a direction 190 degrees counterclockwise from the positive x axis. Write the vector in component form, and show your answers accurate to 3 decimal places.

Chapter 3 Solutions

Finite Mathematics and Calculus with Applications (10th Edition)

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...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

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.

Concept explainers

Videos

To find: The maximum total area.

Want to see the full answer?

Chapter 3 Solutions