Chapter 2.7, Problem 20P

(a) Develop a model that minimizes semivariance for the Hauck Financial data given in the file HauckData with a required return of 10%. Assume that the five planning scenarios in the Hauck Financial rvices model are equally likely to occur. Hint: Modify model (8.10)-(8.19). Define a variable d, for each scenario and let d₂ > R - R¸ with d ≥ 0. Then make the objective function: Min Let FS = proportion of portfolio invested in the foreign stock mutual fund IB = proportion of portfolio invested in the intermediate-term bond fund LG = proportion of portfolio invested in the large-cap growth fund LV = proportion of portfolio invested in the large-cap value fund SG = proportion of portfolio invested in the small-cap growth fund SV = proportion of portfolio invested in the small-cap value fund R = the expected return of the portfolio R = the return of the portfolio in years. Min s.t. R₁ R₂ = R₁ R R5 = FS + IB + LG + LV + SG + SV = R₂ R d₁ =R- d₂z R- d₂ ZR- d₁R- d≥R- R = FS, IB, LG, LV, SG, SV…

The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin-Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas. The following is a linear program used to determine which cities Martin-Beck should construct a plant in. Let y₁ = 1 if a plant is constructed in Detroit; 0 if not y₂ = 1 if a plant is constructed in Toledo; 0 if not y₂ = 1 if a plant is constructed in Denver; 0 if not y = 1 if a plant is constructed in Kansas City; 0 if not. The variables representing the amount shipped from each plant site to each distribution center are defined just as for a transportation problem. *,, = the units shipped in thousands from plant i to distribution center j i = 1 (Detroit), 2 (Toledo), 3 (Denver), 4 (Kansas City), 5 (St.Louis) and…

Consider the following mixed-integer linear program. Max     3x1  +  4x2 s.t.   4x1  +  7x2  ≤  28   8x1  +  5x2  ≤  40 x1, x2 ≥ and x1 integer (a) Graph the constraints for this problem. Indicate on your graph all feasible mixed-integer solutions. On the coordinate plane the horizontal axis is labeled x1 and the vertical axis is labeled x2. A region bounded by a series of connected line segments, and several horizontal lines are on the graph. The series of line segments connect the approximate points (0, 4), (3.889, 1.778), and (5, 0). The region is above the horizontal axis, to the right of the vertical axis, and below the line segments. At each integer value between 0 and 4 on the vertical axis, a horizontal line extends out from the vertical axis to the series of connect line segments.   On the coordinate plane the horizontal axis is labeled x1 and the vertical axis is labeled x2. A region bounded by a series of connected line segments, and several…

Consider the nonlinear optimization model stated below. Min s.t. 2x²-18x + 2XY + y² - 14Y + 53 x + 4Y ≤ 8 (a) Find the minimum solution to this problem. |at (X, Y) = (b) If the right-hand side of the constraint is increased from 8 to 9, how much do you expect the objective function to change? Based on the dual value on the constraint X + 4Y ≤ 8, we expect the optimal objective function value to decrease by (c) Resolve the problem with a new right-hand side of the constraint of 9. How does the actual change compare with your estimate? If we resolve the problem with a new right-hand-side of 9 the new optimal objective function value is| , so the actual change is a decrease of rather than what we expected in part (b).

Statement:If 2 | a and 3| a, then 6 a. So find three integers, and at least one integer should be negative. For each of your examples, determine if the statement is true or false.

Statement: If 4 | a and 6 | a, then 24 | a. So find three integers, and at least one integer should be negative. For each of your examples, determine if the statement is true or false.

2) dassify each critical point of the given plane autovers system x'=x-2x²-2xy y' = 4y-Sy³-7xy