Homework Answers
2. The area of a rectangle with vertices (±x, ±y) is 4xy. Use Langrange multipliers to find the maximum area of such a rectangle with vertices on the ellipse 4x 2 + y 2 = 32 2. The area of a rectangl...
2. The area of a rectangle with vertices (±x, ±y) is 4xy. Use
Langrange multipliers to find the maximum area of such a rectangle
with vertices on the ellipse 4x 2 + y 2 = 32
2. The area of a rectangle with vertices (trty) is 4xy. Use Langrange multipliers to find the maximum area of such a rectangle with vertices on the ellipse 412 + y2-32.
2. The area of a rectangle with vertices (trty) is 4xy. Use Langrange...
1. Find the absolute maximum and minimum values of f(r,y) = x2+y2+5y on the disc {(x,...
1. Find the absolute maximum and minimum values of f(r,y) = x2+y2+5y on the disc {(x, y) | x2+y2 < 4}, and identify the points where these values are attained 2. Find the absolute maximum and minimum values of f(x, y) = x3 - 3x - y* + 12y on the closed region bounded by the quadrilateral with vertices at (0,0), (2,2), (2,3), (0,3), and identify the points where these values are attained. 3. A rectangular box is to have...
Maximize P = 4x + 5y subject to 2x + y < 50 2 + 3y...
Maximize P = 4x + 5y subject to 2x + y < 50 2 + 3y < 75 2 > 0 y > 0 Identify the feasible region as bounded or unbounded: List the corner points of the feasible region, separated by a comma and a space. If the region is unbounded, create appropriate ghost points and list those as well. For each corner point, list the value of the objective function at that point. The format should be (x1,y1)...
Please show work!! (1 point) Take the system x' = 4x – xy, y = 5y...
Please show work!!
(1 point) Take the system x' = 4x – xy, y = 5y + x2. How many critical points are there? What is the critical point with the largest x-coordinate? ( The linearization at this point is | tion at this point is [*] =A (Where A is where A is ul A = At this point the behavior is For behavior write one of "saddle", "source", "sink", "spiral sink", "spiral source", "center".
A company produces two types of solar panels per year: x thousand of type A and...
A company produces two types of solar panels per year: x thousand of type A and y thousand of type B. The revenue and cost equations, in millions of dollars, for the year are given as follows. R(x,y) = 4x + 5y C(XY) x2 - 4xy+By2 + 12x - 51y-2 Determine how many of each type of solar panel should be produced per year to maximize profit. The company will achieve a maximum profit by selling solar panels of type...
Given the following linear program that maximizes revenue (assume x and y cannot be negative): Max...
Given the following linear program that maximizes revenue (assume x and y cannot be negative): Max Z = 15x + 20y s.t. 5x + 5y ≤ 40 4x + y ≤ 4 What is the maximum revenue at the optimal solution? $185 $120 $80 $200
10. Given a system of equations x + y + z = 200 4x + 5y...
10. Given a system of equations x + y + z = 200 4x + 5y + 72 = 1000 x – 2y = 0 (a) Using what you learned so far in your major, give an example of how this system of equations can be applied. (b) Without a calculator, please solve the system of equation.
f(1,y) = x² + 4xy + y2 – 2.c + 2y +1. f(x,y) has a horizontal...
f(1,y) = x² + 4xy + y2 – 2.c + 2y +1. f(x,y) has a horizontal tangent 1. Find all points (a,b,c) where the graph z = plane (parallel to the xy-plane). 0 has a horizontal 2. Find all points (a,b) where the level curve f(x,y) tangent line (parallel to the z-axis).
Please box/circle answers Find the extreme values of the function F(x, y) = 3x2 + 5y?...
Please box/circle answers
Find the extreme values of the function F(x, y) = 3x2 + 5y? on the circle EXAMPLE 2 x2 + y2 = 1. SOLUTION We are asked for extreme values of f subject to the constraint 9(x, y) = x2 + y2 = 1. Using Lagrange multipliers, we solve the equations VF Ug and 9(x, y) = 1, which can be written as fx = 1gx fylgy (x,y) = 1 or as = 2x1 = 2ya x2...
Consider the surface defined by 2 = f(x,y), where f(x, y) = (x + y2 -...
Consider the surface defined by 2 = f(x,y), where f(x, y) = (x + y2 - 1)(x + y - 4). (a) In three separate diagrams draw the level sets of the function at C=2, C = 4, and C= 6. State the coordinates of any isolated points and the radii of any circles that make up these level sets. (Hint: To get an idea of what the surface looks like it might help to look at the curves f(0,y)...
2. The area of a rectangle with vertices (±x, ±y) is 4xy. Use
Langrange multipliers to find the maximum area of such a rectangle
with vertices on the ellipse 4x 2 + y 2 = 32
2. The area of a rectangle with vertices (trty) is 4xy. Use Langrange multipliers to find the maximum area of such a rectangle with vertices on the ellipse 412 + y2-32.
2. The area of a rectangle with vertices (trty) is 4xy. Use Langrange...
1. Find the absolute maximum and minimum values of f(r,y) = x2+y2+5y on the disc {(x, y) | x2+y2 < 4}, and identify the points where these values are attained 2. Find the absolute maximum and minimum values of f(x, y) = x3 - 3x - y* + 12y on the closed region bounded by the quadrilateral with vertices at (0,0), (2,2), (2,3), (0,3), and identify the points where these values are attained. 3. A rectangular box is to have...
Maximize P = 4x + 5y subject to 2x + y < 50 2 + 3y < 75 2 > 0 y > 0 Identify the feasible region as bounded or unbounded: List the corner points of the feasible region, separated by a comma and a space. If the region is unbounded, create appropriate ghost points and list those as well. For each corner point, list the value of the objective function at that point. The format should be (x1,y1)...
Please show work!!
(1 point) Take the system x' = 4x – xy, y = 5y + x2. How many critical points are there? What is the critical point with the largest x-coordinate? ( The linearization at this point is | tion at this point is [*] =A (Where A is where A is ul A = At this point the behavior is For behavior write one of "saddle", "source", "sink", "spiral sink", "spiral source", "center".
A company produces two types of solar panels per year: x thousand of type A and y thousand of type B. The revenue and cost equations, in millions of dollars, for the year are given as follows. R(x,y) = 4x + 5y C(XY) x2 - 4xy+By2 + 12x - 51y-2 Determine how many of each type of solar panel should be produced per year to maximize profit. The company will achieve a maximum profit by selling solar panels of type...
10. Given a system of equations x + y + z = 200 4x + 5y + 72 = 1000 x – 2y = 0 (a) Using what you learned so far in your major, give an example of how this system of equations can be applied. (b) Without a calculator, please solve the system of equation.
f(1,y) = x² + 4xy + y2 – 2.c + 2y +1. f(x,y) has a horizontal tangent 1. Find all points (a,b,c) where the graph z = plane (parallel to the xy-plane). 0 has a horizontal 2. Find all points (a,b) where the level curve f(x,y) tangent line (parallel to the z-axis).
Please box/circle answers
Find the extreme values of the function F(x, y) = 3x2 + 5y? on the circle EXAMPLE 2 x2 + y2 = 1. SOLUTION We are asked for extreme values of f subject to the constraint 9(x, y) = x2 + y2 = 1. Using Lagrange multipliers, we solve the equations VF Ug and 9(x, y) = 1, which can be written as fx = 1gx fylgy (x,y) = 1 or as = 2x1 = 2ya x2...
Consider the surface defined by 2 = f(x,y), where f(x, y) = (x + y2 - 1)(x + y - 4). (a) In three separate diagrams draw the level sets of the function at C=2, C = 4, and C= 6. State the coordinates of any isolated points and the radii of any circles that make up these level sets. (Hint: To get an idea of what the surface looks like it might help to look at the curves f(0,y)...
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