a) Consider the following binary integer programing (BIP) problem: Minimize z = 5x₁ + 6x₂ + 7x3 + 8x4 +9x5 subject to 3x₁x2 + x3 + x₁-2x522 x₁ + 3x2-x3-2x4+xs 20 -x₁-x₂ + 3x3 + x + xs ≥ 1 X1, X2, X3, X4, X5 = 0 or 1, Use the BIP branch and bound (B&B) algorithm and draw the trees of sub-problems used in finding the solution.
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- minimize Z = 5x1 + x2 subject to 3x1 + 4x2 = 24 0 x1 x1 + 3x2Scenario You are going to plant a rectangular flower bed consisting of tulips in the middle surrounded by daisies on the outside. You have the same amount of each flower and will need an equal area for each. You want the border of daisies to be uniform around the tulips in the middle, as shown in the diagram below:A survey was conducted to 12 first time voters on their preferred candidate. The results are: BBM, BBM, LR, IM, PL, PL, IM, IM, BBM, BBM, LR, LR. Which statement is true? The Borda score of PL is two points. BBM wins by plurality method. The Condorcet winner is IM. The modes are LR and IM Which of the following is a property of all linear programming problems? alternate courses of action to choose from minimization of some objectives a computer program usage of graphs in the solution
- Q1 Find the best solution for the following model using simplex MAX Z = 10X1 + 8X2 SUB TO: 4X1 + 2X2 < 80 X1 + 2X2 < 50 X1 2 0,X2 2 0Show that any 2 *2 matrix A that does not have aninverse will have det A= 0.4 For each of the following, determine the direction in which the objective function increases: a z = 4x, - x2 b z = -x, + 2x2 C z = -x - 3x2
- A mixture of pellets is to be made containing x regular pellets, y large pellets and z extra large pellets. Cost, weight and volume data for each type of pellet are shown in the table. Is it possible to make mixture of 55 pellets at a cost of $0.85 if the mixture is to have 120 weight units and 130 volume units? If so, how many each type of pellet should be in the mixture? Pellet Type 5. Number of Cost per Pellet in Cents Weight Units per Pellet Volume Pellets Units per Pellet Regular Large Extra large 2 1 4 y 1 4 3Which of the following types of mortgage loans is presumed to feature points or fees not excending 3%, a maximum term not to exceed 30 years, and no risky features (such as negative amortization, interest-only, or balloon loans)? A) A qualified mortgage B) A conventional mortgage C) A non-qualified mortgage D) A home equity line of credit (HELOC) mortgageWhat combination of x and y will yield the optimum for this problem? Maximize Z = $3x + $15y Subject to: Multiple Choice x= 0, y=4 x= 0, y=3 x= 0, y=0 x= 2y=0 O x=1,y=25 2x + 4y ≤ 12 5x + 2y ≤ 10