Consider the following. Xi' = 3x1 - 2x2 x1(0) = 3 xz' = 2x1 – 2x2,...
7. Systems of first order equations higher order. Consider the system can sometimes be transformed into a single equation of xf xx12x2 = -2x1 + X2, (a) Solve the first equation for x2 and substitute into the second equation, thereby obtain- ing a second order equation for x1. Solve this equation for x1 and then determine x2 also (b) Find the solution of the given system that also satisfies the initial conditions x\ (0) = 2, x2 (0)= 3
Consider the linear system x1 + x2 – 2x3 + 3x4 = 0 2x1 + x2 - 6x3 + 4x4 -1 3x1 + 2x2 + px3 + 7x4 -1 X1 – X2 – 6x3 24 = t. Find the conditions (on t and p) that the system is consistent, and inconsistent. If the system is consistent, find all the possible solutions (including stating the dimension of the solution space(s) and describe the solution space(s) in parametric form).
Min Z = 6X1 + 4x2 Subject to Xi + 2x2 > 2 -X1 + 2x2 5 4 3x1 + 2x2 < 12 X1, X2 > 0
b. x'j(t) = xi(t) – 2x2(t); X'z(t) = 2x1(t) + x2(t); x1(0) = 0, x2(0) = 4 2
2) 17pt) Solve the following IVP. Xi' = -X1 + (3/2)x2 x1(2) = 1 xz' = (-1/6)x1 - 2x2 X2(2) = 0
Consider the mathematical program max 3x1 x2 +3x3 s.t. 2X1 + X2 + X3 +X4-2 x1 + 2x2 + 3x3 + 2xs 5 2x1 + 2x2 + x3 + 3x6 = 6 Three feasible solutions ((a) through (c)) are listed below. (b) xo) (0.9, 0, 0, 0.2,2.05, 1.4) (c) xo) (0.3, 0.1, 0.4, 0.9, 1.65, 1.6) Please choose one appropriate interior point from the list, and use the Karmarkar's Method at the interior point and determine the optimal solution.
Consider the following Linear Problem Minimize 2x1 + 2x2 equation (1) subject to: x1 + x2 >= 6 equation (2) x1 - 2x2 >= -18 equation (3) x1>= 0 equation (4) x2 >= 0 equation (5) 13. What is the feasible region for Constraint number 1, Please consider the Non-negativity constraints. 14. What is the feasible region for Constraint number 2, Please consider the Non-negativity constraints. 15. Illustrate (draw) contraint 1 and 2 in a same graph and find interception...
Consider the following LP problem: Minimize Cost = 3x1 + 2x2 s.t. 1x1 + 2x2 ≤ 12 2x1 + 3 x2 = 12 2 x1 + x2 ≥ 8 x1≥ 0, x2 ≥ 0 A) What is the optimal solution of this LP? Give an explanation. (4,0) (2,3) (0,8) (0,4) (0,6) (3,2) (12,0) B)Which of the following statements are correct for a linear programming which is feasible and not unbounded? 1)All of the above. 2)Only extreme points may be optimal....
Please write neatly and clear. Thanks in advance. 3. Consider the following system of equations: x1 + 2x2-1x3 + 9x4 =1 -2x1 4x2 3x2-4x3 -3x1 +4x2 + 3x3-713 Find the solution (if there is one) to the system of equations. Define if the system is consistent or inconsistent. Give a geometric description of the solution if it exists a. b. c. 3. Consider the following system of equations: x1 + 2x2-1x3 + 9x4 =1 -2x1 4x2 3x2-4x3 -3x1 +4x2 +...
Second order systems of ordinary differential equations (ODE) often describe motional systems involving multiple masses. Solve the following second order system of ODE using Laplace transform method: Xy-=5x1-2x2 + Mu(t-1) x2-=-2x1 + 2x2 x,(t) and x2(t) refer to the motions of the two masses. Consider these initial conditions: x1 (0) = 1, x; (0)-0, x2(0) = 3, x(0) 0 Second order systems of ordinary differential equations (ODE) often describe motional systems involving multiple masses. Solve the following second order system...