Use the Big-M method to find an initial basic feasible solution for the following LP: max z = 3x1 + x2 X1 + x2 2 3 2x1 + x2 < 4 s.t. X1 + x2 = 3 X1, X2 2 0
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A: THE ANSWER IS AS BELOW:
Q: A firm has prepared the following binary integer program to evaluate a number of potential locations…
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please don't use an online calculator.. they confuse me.
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- Solve Problem 1 with the extra assumption that the investments can be grouped naturally as follows: 14, 58, 912, 1316, and 1720. a. Find the optimal investments when at most one investment from each group can be selected. b. Find the optimal investments when at least one investment from each group must be selected. (If the budget isnt large enough to permit this, increase the budget to a larger value.)Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Maximize C = 13x + 3y subject to 12x + 14y ≤ 21 15x + 20y ≤ 37 and x ≥ 0, y ≥ 0. What is the optimal value of x?Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Minimize C = 11x + 5y + 10z subject to 8x + 12y + 19z ≥ 68 13x + 16y + 5z ≥ 136 and x ≥ 0, y ≥ 0, z ≥ 0. What is the optimal value of x? What is the optimal value of y? What is the optimal value of z? What is the minimum value of the objective function?
- Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Maximize C = 14x + 13y + 5z subject to 9x + 11y + 18z ≤ 61 14x + 15y + 12z ≤ 122 and x ≥ 0, y ≥ 0, z ≥ 0. What is the optimal value of x? What is the optimal value of y? What is the optimal value of z? What is the maximum value of the objective function?Draw a graph that identifies the feasible region for the following set of constraints. 0.25 A + 0.25 B ≥ 30 0.5 A + 5 B ≥ 200 0.75 A + 1.5 B ≤ 150 A, B ≥ 0Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Minimize C = 17x + 19y subject to 8x + 14y ≥ 21 11x + 6y ≥ 31 and x ≥ 0, y ≥ 0. What is the optimal value of x and y? What is the minimum value of the objective function? Please show me step by step how to do this by hand, not through excel.
- Consider the following linear programming problem: Min Z = 50x1 + 60x2 s.t. 6x1 + 5x2 >= 30 8x1+4x2 >= 32 x1,x2 >=0. What is the Z in the optimal point of this problem? a. 200 b. 250 c. 300 d. 350 e. none of the abovSolve the following LP by using Excel. State the Optimal Solution and the Objective Function Value. Maximize profit = 910X + 1000Y Subject to: 18X + 20Y ≤ 1,200 360X + 400Y ≤ 30,000 X, Y ≥ 0Given this linear programming model, solve the model and then answer the questions that follow. Maximize Z = 12x1 + 18x2 + 15x3 where x1 = the quantity of product 1 to make, etc. Subject to Machine: 5x 1 + 4x 2 + 3x 3 ≤ 160 minutes Labor: 4x1 + 10x2 + 4x3 ≤ 288 hours Materials: 2x 1 + 2x2 + 4x3 ≤ 200 pounds Product 2: x2 ≤ 16 units x1, x2, x3 ≥ 0 a) Are any constraints binding? If so, which one(s)? b) If the profit on product 3 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain. c) If the profit on product 1 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain. d) If 10 hours less of labor time were available, what would the values of the decision variables be? The objective function? Explain. e) If the manager decided that as many as 20 units of product 2 could be produced (instead of 16), how much additional profit would be generated? f) If profit per unit on each…
- A decision problem has the following three constraints: 70X + 6Y <= 420; 24X + 3Y= 72; and 11X - Y <= 14 . The objective function is Min 17X + 38Y . The objective function value is : a. 338 b. 676 c. unbounded d. infeasible e. 0Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Minimize C = 8x + 8y subject to 7x + 9y ≥ 16 10x + 10y ≥ 22 and x ≥ 0, y ≥ 0. What is the optimal value of x? What is the optimal value of y? What is the minimum value of the objective function?Compute the objective function value for the following problem: Min 30X + 150Y subject to : 2X>=0 ;2X + 10Y = 20; X+Y>=0 a. 0 b. 54 c. infeasible d. 300 e. unbounded