Complete parts a through f below to find nonnegative numbers x and y that satisfy the given requirements. Give the optimum value of P. x+y= 75 and P =xy is maximized dP d. Find dx dP Solve the equation dx = 0. dP dx Solve the equation. (Use a comma to separate answers as needed.) e. Evaluate P at any solutions found in part d, as well as the endpoints of the domain found in part c. Find P(0). P(0) = 0 (Simplify your answer.) Determine P(50). P(50) = || |(Simplify your answer.) More (1,1)

Q: Find the extreme values of f subject to both constraints. (If an answer does not exist, enter DNE.)…

A: Find extreme values of f subject to both constraintsf(x,y,z)=yz+xy;     xy=1;     y2+z2=1

Q: 2. Solve and state the largest interval over which the general solution is defined: dy (1+2)- ry…

A:

Q: Solve the Leontief production equation for an economy with three sectors, given the following. 0.3…

A: Given that C=0.30.300.20.60.20.100.3 and d=206070 The matrix equation that represents the Leontief…

Q: 2. Solve and state the largest interval over which the general solution is defined: dy (x+ 2)´ Jr =…

A: Answer

Q: 3. Consider in R? the straight line l of equation y = 2.x +1 and the point P = (1, -1). (a) Use the…

A: Lagranges Multipliers Method

Q: Use techniques of optimization to determine which point on the line (0,0). That is, what point on…

A: The solution of given problem is as below :

Q: To find the maximum value of the function xyz by Lagrange method of multipliers under the…

A:

Q: 2.2 The value of xe*dx by using the two-point Gauss quadrature is most nearly 0.2 (A) 11.672 (B…

A:

Q: Follow the steps below to find the nonnegative numbers x and y that satisfy the given requirements.…

A: Given problem:- x + y = 250 and the product P = xy as large as possible.

Q: Маx Z Z = 4x1 + 2x2 s.t. s.t. 2х1 + 3x, < 13 x2 2 2 X1 2 2 X1,X2 20 a) Solve graphically. b) What…

A:

Q: r'ydx+(x* + x*y° + y*\dy = 0

A: See the details solution in below

Q: It is easy to check that for any value of c, the function y = ce-2 + e¬ is a solution of the…

A: This question is based on substitution.

Q: Using x cubic centimeter(cc) of a certain drug, the resulting blood pressure B(xX) is approximated…

A: We have to calculate maximum blood pressure

Q: x + 2y 2 8 (y 20 Minimum for nur C = x + 3y

A: Linear programming problem: graphical method. The given objective function is C=x+3y, subjected to…

Q: Find maximum and minumum values of f(x, y, z) = 9x – 18y +45z subject to the constraint x? + y² + z²…

A:

Q: Use Stefffensen's method to approximate the solution of the fixed point equation æ 23 – 0.5z – 1.7…

A: Consider the given equation as x=x3-0.5x-1.7x2+25.5

Q: Let A and Abe the maximum and minimum values, respectively of the function f (x, y) = 4x +y? subject…

A:

Q: Q1/ solve the following by using graphical method: Maximize Z=12x+16y, Subject to: 10x+20y < 120,…

A:

Q: 1. Find the maximum and minimum points of the given equation: a. y = x3 - 3x b. у%3D (x - 6)?(9— х)

A: Given: a.y=x3-3x

Q: Solve the following Euler-Cauchy type equation: 1 (x² D² + 3xD+ 1)y = - 3xD+ 1)y = (1 – x)² ' d…

A: Given equation is, x2D2+3xD+1y=1(1-x)2 Take, (x2D2+3xD+1)y=0 Then assume, y=xn,…

Q: With the understanding that D = , find a complete solution of the dt following: (D + 5)x + (D + 3)y…

A: Given: D+5x+D+3y=e-t      ....(1)and   D+2x+D+1y=3        ....(2)On solving (1) and (2) we…

Q: Solve the following L.P using graphical method. Maximize Z= 3a + 2b la + 1b 0. Find the optimum zone…

A: See the solution in the  given fig.

Q: Find maximum and minumum values of f(x, y, z) = 8x – 16y + 40z subject to the constraint x? + y? +…

A: The given function is; f(x,y,z) = 8x-16y+40z

Q: Section A : Solve the boundary value problem d²y = x+ 2y, with the boundary conditions dx² Y(0)=0…

A:

Q: Find the maximum of 2x + 3y on the feasible set given by x2 0, y 20, 2x + y 22, 3x + 4y s 12. a) 6…

A: We sketch 2x+y≥2 , 3x+4y≤12 , x≥0, y≥0 using a graphing calculator.

Q: Find values of m so that the function y = e"™x is a solution of the given D а) y' + 2y = 0 b) y" –…

A: Using differential equations ,

Q: Find and graph the solution to the IVP y'+ p(x)y = 0, y(0) = 3 %3D Where if 0 < x < 1 if 1 < x < 3…

A:

Q: If (V1,V2) is a fundamental set of solutions for the DE: t?y" - 3y' + costy =0 and if W(v1.V2)(1)=2,…

A:

Q: with the understanding that D = find a complete solution of the following: (2D + 1)x + (D + 1)y = 3

A: Given that…

Q: In p(x,y) = 3ry – x* – y°, x is the average daylight and y is the average daily rainfall. %3D Solve…

A: To find the points that maximize the the productivity of the function px, y=3xy-x3-y3

Q: Question 13 The cost, C. in dollars to hire pavers to pave the parking lot at a shopping mall can be…

A: Given Data: The cost to hire the pavers is: C=5x2-50x+1200 For the minimum cost, the derivative of…

Q: It is easy to check that for any value of c, the function y = ce + e is a solution of the equation…

A: y=ce-2x+e-xSubstitute x=-4 and y=10 into the above equation.

Q: find a set of solutions unless the statement of the exercise stipulates otherwise use any method in…

A: Let us consider the differential equation M(x,y)dx+N(x,y)dy=0 Now, if ∂M∂y=∂N∂x that is if the…

Q: "Use the northwest corner method to find the starting solution, then determine the optimum solution…

A: To find the starting and the optimum solution of the given problem using northwest corner method.…

Q: Q7) by using the (graphical method) find the optimum solution of X1, X2 that the maximum Z=5X+7Y…

A: Answer is given below.

Q: Write the KKT conditions and find the optimal solution (x,y) for the following problem. Minimise 2x…

A: Given that,                Mini     2x-y2+2ysubjected to     y=-3x,                           x≤1,…

Q: Solve the following L.P using graphical method. Maximise Z = 3a + 2b S.T. 1a + 1b ≤ 4        1a –…

A: The given linear programming problem is  Max z=3a+2ba+b≤4a-b≤2a,b≥0 The given problem can be solved…

Q: Use Lagrange multipliers to find the maximum and minimum values of f(x,y) = x² + y?; subject to x? –…

A: Given, f(x,y)=x2+y2; subject to x2+y2-2x-4y=0. We have to find the maximum and minimum value of the…

Q: Find the extremum of f(x.y) subject to the given constraint, and state whether it is a maximum or a…

A: The given function is, fx,y,z=x2+y2+z2 Consider another function g(x) from the constraint equation,…

Q: Use the method of Lagrange multipliers to optimize the function f(x, y) = xy subject to the…

A:

Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = 2x – y subject to the…

A:

Q: It is easy to check that for any value of c, the function y - 2x = ce +e-* is a solution of the…

A:

Q: C = C(x) = (Hint: V = a²y) C' (x) = Solving C' = 0 yields that value of x that minimizes the cost.…

A:

Q: (d) Find the maximum and minimum values of the function f(x, y, z) = yz + x? subject to the…

A: Introduction: When a multivariable function is to be extremized under certain constraints, we follow…

Q: : Ebobl Qf solve the initiat Valu problem %3esince-2) y(an2) =a

A:

Q: (Round to 2 decimals when needed) Solve for the optimal x*, y*, and 1* of the following problem:…

A:

Q: Sketch an approximate solution curve that passes through each of the indicated points

A: Here is the solution of the given problem.

Q: Find the value of x and y which satisfy 2x + 3y = 8 and whose product is a minimum. a. 1 and 2…

A: we have to find

Q: A fundamental solution set for the D.E. y(4) – y" – 12y = 0 %3D

A:

Q: The Crank-Nicolson method used to solve parabolic PDES is stable for a. A# 1/2 O b. all values of A…

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: