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- 23. Consider the following constraints from a two-variable linear program: X ≥ 1; Y ≥ 1; X + Y ≤ 9. If these are the only constraints, which of the following points (X, Y) CANNOT be the optimal solution? Part 2 A. (1, 8) B. (8, 1) C. (4, 4) D. (1, 1) E. The question cannot be answered without knowing the objective function.The network below shows the flows possible between pairs of six locations. A graph with 6 nodes and 13 directed arcs is shown. Node 1 is connected to node 2 by arc of value 17, to node 3 by arc of value 19, and to node 5 by arc of value 9. Node 2 is connected to node 3 by arc of value 8 and to node 4 by arc of value 14. Node 3 is connected to node 2 by arc of value 5, to node 4 by arc of value 9, to node 5 by arc of value 7, and to node 6 by arc of value 24. Node 4 is connected to node 3 by arc of value 9 and to node 6 by arc of value 13. Node 5 is connected to node 3 by arc of value 7 and to node 6 by arc of value 11. Node 6 has no directed arcs directed to other nodes. Formulate an LP to find the maximal flow possible from node 1 to node 6. (Let xij represent the flow from node i to node j. Enter your maximum flows as a comma-separated list of inequalities.) Max s.t.Node 1 Flows Node 2 Flows Node 3 Flows Node 4 Flows Node 5 Flows Node 6 Flows…A company supplies goods to three customers, who eachrequire 30 units. The company has two warehouses.Warehouse 1 has 40 units available, and warehouse 2 has 30units available. The costs of shipping 1 unit from warehouseto customer are shown in Table 7. There is a penalty for eachunmet customer unit of demand: With customer 1, a penaltycost of $90 is incurred; with customer 2, $80; and withcustomer 3, $110. Formulate a balanced transportationproblem to minimize the sum of shortage and shipping costs.
- To formulate a minimization problem for solution by the simplex method, we must add slack variables to a. only inequality constraints. b. only “less than” constraints. c. only “greater than” constraints. d. all inequality constraints.Consider the following set of constraints (Maixmization problem): 43X+ 86Y>= 29, and 129X+ 43Y >= 14.5. The following is true for this problem: a. Unbounded problem. b. X = 0, Y = 43 is the only optimal solution. c. X=43, Y=-7 is the only optimal solution. d. Infeasible problem. Clear my choiceGiven 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…
- 4. Consider the following linear programming problem: Maximize Z=$15x + $5y, subject to (1) 2x + y ≤ 10 and (2) 4x + 3y ≤ 24 and (3) x, y ≥ 0. Will the optimal solution change if the objective function becomes Maximize Z=$15x + $20y (constraints remain the same)? Select one: a. Can't determine given the information. b. Yes, it will change. c. No, it remains the same.XYZ Corporation operates two plants, each of which has a capacity of 140 units per day. Each day, XYZ must ship their product to each of four customers. Customers A, B, and C each have a demand of 11 units per day while customer D has a demand of 247 units per day. The cost of shipping one unit of each product from each of the two plants to each of the customers is shown in the table below. Customer A Customer B Customer C Customer D Plant 1 12 18 21 10 Plant 2 16 14 18 20 How many units should XYZ ship from each plant to each customer? Customer A Customer B Customer C Customer D Plant 1 Plant 2 What is the least XYZ will spend on shipping each day?Suppose you own 11 bronze coins worth a total of $150,11 silver coins worth a total of $160, and 11 gold coinsworth a total of $170. Develop a linear integer model tofind a combination of coins worth exactly $110
- Solve the following Linear programming problem using the simplex method:Maximize Z = 10X1 + 15X2 + 20X3subject to:2X1 + 4X2 + 6X3 ≤ 243X1 + 9X2 + 6X3 ≤ 30X1, X2 and X3 ≥ 0(b) Suppose X1, X2, X3 in (a) refer to number of red, blue, and green balloons respectivelywhich are produced by a company per day. And Z is the total profit obtained afterselling these balloons. Interpret your answer obtained in (a) above(c) Write the dual of the following linear programming problem:Minimize Z = 2X1 − 3X2 + 4X3subject to:3X1 + 4X2 + 5X3 ≥ 96X1 + X2 + 3X3 ≥ 47X1 − 2X2 − X3 ≤ 105x1 − 2X2 + X3 ≥ 34X1 + 6X2 − 2X3 ≥ 3X1, X2 and X3 ≥ 0Consider the following LP problem: Min 6X+ 27Y Subject to : 2 X + 9Y => 25, and X + Y <= 75. Pick a suitable statement for this problem: a. X=37.5, Y=37.5 is the only optimal solution. b. Optimal Obj. function value is 75 c. X = 0, Y = 0 is the only optimal solution. d. Optimal Obj. function value is 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 toMachine 5x1 + 4x2 + 3x3 ≤ 160 minutes Labor 4x1 + 10x2 + 4x3 ≤ 288 hoursMaterials 2x1 + 2x2 + 4x3 ≤ 200 poundsProduct 2 x2 ≤ 16 units x1, x2, x3 ≥ 0 a. Are any constraints binding? If so, which one(s)?