8 Minimize z= x + 3y 9 + 22 54 + 4yΣ Subject to 2y + 2 > ΛΙ ΛΙ ΛΙΛΙ ΛΙ 14 O Σ Ο Minimum is Maximize z = 4x + 2y 32 + 4y < < 32 5x + 5y < Subject to 0 VI VI ALAI y 0 Maximum is
3. Suppose x,y,z satisfy the competing species equations <(6 - 2x – 3y - 2) y(7 - 2x - 3y - 22) z(5 - 2x - y -22) (a) (6 points) Find the critical point (0,Ye, ze) where ye, we >0, and sketch the nullclines and direction arrows in the yz-plane. (b) (6 points) Determine if (0, yc, ze) is stable. (c) (8 points) Determine if the critical point (2,0,0) is stable, where I > 0.
Solve the linear programming problem by simplex method. . Minimize C= -x - 2y + z. subject to 2x + y +2 < 14 4x + 2y + 3z < 28 2x + 5y + 5z < 30 x = 0, y>02 > 0
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)...
QUESTION 3 Given this problem: Max Z = $0.3x + $0.90y Subject to: 2x + 3.2y <= 160 4x + 2.0y <= 240 y <= 40 X, y >=0 a) Solve for the quantities of x and y which will maximize Z. The x = The y = b) What is the maximum value of Z? The Z=
(1 point) Find the minimum and maximum of the function z-6x - 4y subject to 6x-3y 15 6x +y < 49 What are the corner points of the feasible set? The minimum is and maximum is . Type "None" in the blank provided if the quantity does not exist.
Let Ě =< 2x + 2,3y+z, 6x + 6y > be a vector field in R3. Evaluate the following surface integral directly: xdA || i-dš= $ 8. (XFL) S Where S is the part of the plane 2x + 3y + z = 6 in the first octant (with upward orientation). SHOW ALL OF YOUR WORK!
Use the information below to create the initial simplex tableau. Maximize Z 10x1 + 4x2 subject to %3D 11x1 + 24x2 < 37 27x1 + 30x2 < 61 17x1 + 14x2 25 xi > 0, x2 > 0 0000 0000 0000 0000 VI VI VỊ
find the inverse z transform X(z) = 1-2-3 with [2]<1
PROBLEMS 7.3 1. Minimize Z= 6x + 14y subject to 14x + 7y > 43 3x + 7y > 21 --x+y> -5 x,y > 0 2. Maximize Z= 2x + 2y subject to 2x - y > -4 x - 2y < 4 x+y = 6 Xy0