12. Find the minimum value of f(x1,x2 ubject to the constraint 121 12. Find the minimum value of f(x1,x2 ubject to...
3. Find the minimum and maximum values of the function f (x, y) = x2 + y subject to the constraint x y = 162. Use the Lagrange Equations. (Use symbolic notation and fractions where needed.) maximum value of the function| minimum value of the function 3. Find the minimum and maximum values of the function f (x, y) = x2 + y subject to the constraint x y = 162. Use the Lagrange Equations. (Use symbolic notation and fractions...
9. Find the maximum and minimum of f(x,y) = 4.r+10y2 subject to the constraint x2 + y2 = 4.
(3) Let X = (X1, X2) be a two-dimensional random vector with variance Var[X= 121 12] Compute Covſa, Xi +a X2, 6, X1 + b2 X2], where an, az, bi, by are given constants.
Let X1 and X2 have joint PDF f(x1,x2)=x1+x2 for 0 <x1 <1 and 0<x2 <1.(a) Find the covariance and correlation of X1 and X2. (b) Find the conditional mean and conditional variance of X1 given X2 = x2.
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?
Find the minimum value. Minimize subject to C = 10xı + 31x2 - 5x3 X1 + 3x2 s6 4x2 + x3 s2 X1, X2, X3 20 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The minimum value C= occurs at X1 - X2 X3 = OB. There is no solution.
The utility function is u = x1½ + x2, and the budget constraint is m = p1x1 + p2x2. Derive the optimal demand curve for good 1, x1(p1, p2), and good 2, x2(m, p1, p2). Looking at the cross price effects (∂x1/∂p2 and ∂x2/∂p1) are goods x1 and x2 substitutes or complements? Looking at income effects (∂x1/∂m and ∂x2/∂m) are goods x1 and x2 inferior, normal or neither? Assume m=100, p1=0.5 and p2=1. Using the demand function you derived in...
Q4. (Sensitivity Analysis: Adding a new constraint) (3 marks) Consider the following LP max z= 6x1+x2 s.t.xi + x2 S5 2x1 + x2 s6 with the following final optimal Simplex tableau basis x1 r2 S2 rhs 0 0 18 0.5 0.5 0.5 0.5 x1 where sı and s2 are the slack variables in the first and second constraints, respectively (a) Please find the optimal solution if we add the new constraint 3x1 + x2 S 10 into the LP (b)...
Problem 2.14 Use algebraic manipulation to find the minimum product-of-sums expression for the function f= (x1 + x3 + x4) (x1 + x2' + x3) (x1 + x2' + x3' + x4). %3D
6. Consider a consumer with the utility function u(x1,x2) = In(x) x2 and the budget constraint px + p2x2 = m. Derive the consumer's demand functions for x1 and x2. (25 marks)