Linear Programming Practice. A feasible region has vertices at (-1,3),(3,5),(4,-1), and (-1,-2). Find the maximum and minimum values of each function. f(x,y)=x-y f(x,y)=3x+2y f(x,y)=3y-x f(x,y)=-2x-y
Added by Christian A.
Step 1
Let's think step by step. Show more…
Show all steps
Close
Your feedback will help us improve your experience
Ahmad Reda and 86 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find the indicated maximum and minimume values by the linear programming method of this section. For Exercises $5-16,$ the constraints are shown below the objective function. Graphing the constraints of a linear programming problem shows the consecutive vertices of the region of feasible points to be $(0,0),(12,0),(10,7),(0,5),$ and $(0,0) .$ What are the maximum and minimum values of the objective function $F=2 x+5 y$ in this region?
Inequalities
Linear Programming
In Exercises 29-34, the linear programming problem has an unusual characteristic. Sketch a graph of the solution region for the problem and describe the unusual characteristic. Find the minimum and maximum values of the objective function (if possible) and where they occur. Objective function: $ z = x + y $ Constraints: $ \hspace{1cm} x \ge 0 $ $ \hspace{1cm} y \ge 0 $ $ -x + y \le 0 $ $ -3x + y \ge 3 $
Systems of Equations and Inequalities
The graph of the feasible region is shown. f = 8x + 4y The x y coordinate plane is given. Three lines and a shaded region are on the graph. The line 2x + y = 40 enters the window in the first quadrant, goes down and right, crosses the line x + 5y = 100, crosses the line 8x + 5y = 170, and ends on the positive x-axis. The line 8x + 5y = 170 enters the window on the positive y-axis, goes down and right, crosses the line x + 5y = 100, crosses the line 2x + y = 40, and exits the window in the first quadrant. The line x + 5y = 100 enters on the positive y-axis, goes down and right, crosses the line 8x + 5y = 170, crosses the line 2x + y = 40, and exits the window in the first quadrant. The shaded region is below the three lines, above the x-axis, and right of the y-axis. Find the corners of the feasible region. (Order your answers from smallest to largest x, then from smallest to largest y.) (x, y) = (x, y) = (x, y) = (x, y) = (x, y) = Find the maximum and minimum of the given objective function (if they exist). (If an answer does not exist, enter DNE.) maximum f = minimum f =
Sri K.
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD