[1.38] Consider the problem: Minimize cx subject to Axb, x>0. Suppose that one component of the...
Please answer 1.39, I understand 1.38.
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[1.38] Consider the problem: Minimize cx subject to Ax 2b x0. Suppose that one component of the vector b, say b,, is increased by one unit to b a. What happens to the feasible region? b. What happens to the optimal objective value? 1.39 From the results of the previous problem, assuming ôz'lob, exists, 0, 0, or 0?
[1.38] Consider the problem: Minimize cx subject to Ax 2b x0. Suppose that one component...
[5.53] Consider the problem: Minimize cx subject to Ax = b, x 2 0. Let x* be the unique optimal extreme point. Show that the second best extreme point must be adjacent to x*. What happens if the uniqueness assumption is relaxed?
Consider the following LP problem. minimize 3:01 +4.c3 subject to 2:01 + x3 - I3 < -2 21 +3.02 – 5x3 = 7 21 <0,22 > 0, 03 free Which of the LP problem below is its dual problem? maximize -2p1 + 7p2 subject to 2p. + P23 1 + 3p2 50 -P1 - 5p2 = 4 Vi < 0,2 > 0 maximize --2p1 + 702 subject to 2p. + P23 1 + 3p2 50 -P1 - 5p2 = 4...
4. Consider our standard LP: maxc.x subject to Ax <b and x > 0. Assume every entry of A is strictly positive and b > 0. Deduce that the LP has an optimal solution.
#16.2 Consider the following standard form LP problem: minimize 2xi -x2-^3 subject to 3x1+x2+エ4-4 a. Write down the A, b, and c matrices/vectors for the problem. b. Consider the basis consisting of the third and fourth columns of A, or- dered according to [a4, as]. Compute the canonical tableau correspond ing to this basis c. Write down the basic feasible solution corresponding to the basis above, and its objective function value. d. Write down the values of the reduced cost...
Consider the following minimum problem: Minimize: C = 22 Subject to the constraints: 1 +5:03 > 10 -621 +5x2 > 3 X>0 22 > 0 Write the dual problem for the above minimum problem by selecting the appropriate number for each blank box shown below (Do not solve the dual problem). P= (Select) Y1+ (Select) Y2 [ Select) Y1+ (Select) Y2 50 (Select) Yi+ 10 Y2 <1 yı >0; 92 > 0
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4. Consider the following LP: Minimize z = x; +3x2 - X3 Subject to x + x2 + x2 > 3 -x + 2xz > 2 -x + 3x2 + x3 34 X1 X2,43 20 (a) Using the two-phase method, find the optimal solution to the primal problem above. (b) Write directly the dual of the primal problem, without using the method of transformation. (c) Determine the optimal values of the dual variables from the optimal...
Suppose that X is a continuous random variable with density
pX(x) = ( Cx(1 − x) if x ∈ [0, 1] 0 if x < 0 or x > 1.
(a) Find C so that pX is a probability density function.
(b) Find the cumulative distribution of X.
(c) Calculate the probability that X ∈ (0.1, 0.9).
(d) Calculate the mean and the variance of X.
9.) Suppose that X is a continuous random variable with density C(1x) if E...
Exercise 7.3. Consider the nonlinearly constrained problem minimize xER2 to (7.1) a x2 1 = 0. subject 1)T is a feasible path for the nonlinear constraint (a) Show that x(a) x x - 1 = 0 of problem (7.1). Compute the tangent to the feasible path at E = (0, 0)7 (sin a, cos a - + X (b) Find another feasible path for the constraint x? + (x2 + 1)2 - 1 = 0. Compute the tangent to the...
Question 3. Micro Review. Suppose that a firm has a production function Q = kalb, where a>0 and b>0. K is capital and L is labor. Assume the firm is a price taker and takes the prices of inputs, (r and w) as given. 1) Write down the firm's cost minimization problem using a Lagrangean. 2) Solve for the optimal choses of L and K for given factor prices and output Q. 3) Now use these optimal choices in the...