Express the following optimization problem as a standard linear program in matrix notation max zER?, £ER´ p'z +£ subject to the constraints that >0, ro <0 and r¡ < 3.
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Q: optimal integer solution
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- Glenmont Corporation wants to select 1 project from a set of 4 possible projects. Which of these constraints ensures only 1 project is selected? X1 + X2 + X3 + X4 ≥ 0 X1 + X2 + X3 + X4 ≥ 1 X1 + X2 + X3 + X4 = 1 X1 + X2 + X3 + X4 ≤ 1Use the method of Lagrange multiplier to determine the absolute maximum and min-imum values of the function subject to the given constraint.Pls. show complete solution and right answer. Thanks.Find the indicated maximum or minimum value of f subject to the given constraint.
- 7. Use Lagrange multipliers to give an alternate solution. Find two positive numbers whose product is 100 and whose sum is a minimum.Consider the following linear program : z = 6x1 + 6x2 + 10x3 → min s.t. 4x1 + 3x2 + 2x3 ≥ 16 x1 + 2x2 + 5x3 ≥ 16 x1, x2, x3 ≥ 0 a) a) Build the dual problem corresponding to the given problem! b) Solve the dual problem graphically! Determine the exact coordinates by computing the intersection point of two appropriate lines! c) Conclude for the solution (objective and variables) of the primal problem by using the complementary slackness conditions.Use the method of Lagrange Multipliers to find the maximum and minimumvaluesof x2+y2 subject to the constraint x4+ y4=2
- Consider the following all-integer linear program: Max 5x1 + 8x2 s.t. 5x1 + 6x2 ≤ 32 10x1 + 5x2 ≤ 46 x1 + 2x2 ≤ 10 x1, x2 ≥ 0 and integer Choose the correct graph which shows the constraints for this problem and uses dots to indicate all feasible integer solutions. (i) (ii) (iii) (iv) Graph (i) Find the optimal solution to the LP Relaxation. If required, round your answers to two decimal places. x1= fill in the blank 2 x2= fill in the blank 3 Optimal Solution to the LP Relaxation fill in the blank 4 Round down to find a feasible integer solution. If your answer is zero enter “0”. x1= fill in the blank 5 x2= fill in the blank 6 Feasible integer solution fill in the blank 7 Find the optimal integer solution. If your answer is zero enter “0”. x1= fill in the blank 8 x2= fill in the blank 9 Optimal Integer Solution fill in the blank 10Write down the mathematical expressions for: The market-clearing condition when all endowments are owned by a private-sector individual and that an allocation (x, y) must be feasible in a world with private-endowment, but NO production.can you please show an easy way using d’Alembert's reduction of order method to find a second linearlyindependent solution. What is the general solution of the diferentialequation for number 7
- Write down (without solving) the dual LP problem. (Let the variables x, y, and z correspond to the first, second, and third constraints, respectively.)Minimize c = s + 2t + u subject to3s − t + v ≥ 1,000u − v ≥ 2,000s + t ≥ 500s ≥ 0, t ≥ 0, u ≥ 0, v ≥ 0.Maximize p = subject to the following constraints. (Enter your answers as a comma-separated list of inequalities.) x ≥ 0, y ≥ 0, z ≥ 0.Write down (without solving) the dual LP problem. Minimize c = 2s + 2t + 4u subject to s + u ≥ 300 3s + t ≥ 150 s ≥ 0, t ≥ 0, u ≥ 0. Maximize p = 300x+150y subject to the following constraints. (Enter your answers as a comma-separated list of inequalities.) x+3y<2, y<2, x<4 x ≥ 0, y ≥ 0Explain why it is problematic to include a constraintsuch as the following in an LP model for a blendingproblem:Total octane in gasoline 1 blendBarrels of gasoline 1 blended daily$ 10