Please convert it from a second-order equation to two first-order ones.
(Unconstrained Optimization-Two Variables) Consider the function: f(x1, x2) = 4x1x2 − (x1)2x2 − x1(x2)2 Find a local maximum. Note that you should find 4 points that satisfy First Order Condition for maximization, but only one of them satisfies Second Order Condition for maximization.
3. Two solutions of the following linear equation system are x1, X2, where Xi = (1,1,-3,1), x2-x1 + xd xd that makes cTx2 - cTx1 - 1, where c [1 1 2 1] Find every Ax=11 2 2 3 |x=b
3. Two solutions of the following linear equation system are x1, X2, where Xi = (1,1,-3,1), x2-x1 + xd xd that makes cTx2 - cTx1 - 1, where c [1 1 2 1] Find every Ax=11 2 2 3 |x=b
Min 2x1 + x2 s.t. x1 + x2 ≥ 4 x1 – x2 ≥ 2 x1 – 2x2 ≥ –1 x1 ≥ 0, x2 ≥ 0 Please solve the linear program graphically, showing the objective function, all constraints, the feasible region and marking all basic solutions (distinguishing the ones that are feasible).
Consider the following. Xi' = 3x1 - 2x2 x1(0) = 3 xz' = 2x1 – 2x2, *2(0) = (a) Transform the given system into a single equation of second order by solving the first equation for x2 and substitute into the second equation, thereby obtaining a second order equation for X1. (Use xp1 for xı' and xpP1 for x1".) xpP1 – xP1 – 2x1 = 0 (b) Find X1 and x2 that also satisfy the initial conditions. *2(t) =
Along with x1' please solve for
x2'. Thanks!
Transform the given differential equation into an equivalent system of first-order differential equations. y' (t) + 5y' (t) - 6ty(t) = 6 cost Let x, = y and X, Ey. Complete the differential equation for X.
f(x1, x2) = -2(x1)(x2)+ (x1)^3 + (x2)^3 a) Find a maximum in the region where x1 ≤ 1 and x2 ≤ 1 (Hint: remember to check what happens when x1 = 1 and x2 = 1) b) Now consider (x1, x2) ∈ R 2 , that is, the entire two-dimensional space where x1 and x2 are in[−∞,+∞]. Is there a maximum?
a) Solve the following problem using Lagrange multiplier method. Minimize fCX)-x1+ x2+X 4. subject to: x2+x-3 X1+3x2+ 2x)- 7 (1) (2) (Note: Please do not check the second order sufficiency conditions) b) If the right side of the above constraint (1) is changed to 3.4, using sensitivity analysis find the approximate new minimum value of fX).
a) Solve the following problem using Lagrange multiplier method. Minimize fCX)-x1+ x2+X 4. subject to: x2+x-3 X1+3x2+ 2x)- 7 (1) (2) (Note: Please do...
U = 8x10.5+ 2x2, where x1 is the quantity of good 1 consumed, and x2 is the quantity of good 2 consumed. (Yes the x is raised) 8x1.5 Suppose that the consumer has a budget of M = $400 to spend and that good 1 has a price of p1= 2, and good 2 has a price of p2= 8. Answer the following questions, and write your answers in the Answer Sheet. Write the person’s budget constraint as an equation,...
3. Given a second-order ODE, [x1,x2] ER?, study the stability of the equilibrium point at the origin. <=x2–2x17x7 + x3) *2=– *1 –2x2(x} + xž)
3. Two fair, four-sided dice are rolled. Let X1, X2 be the outcomes of the first and second die, respectively. (a) Find the conditional distribution of X2 given that Xi + X2 = 4. (b) Find the conditional distribution of X2 given that Xi + X2-5.