A company wants to locate a new warehouse to minimize the longest distance traveled by any of its delivery trucks. It has 4 stores, and their coordinates are as follows: X-Coordinate Store 1 Store 2 Store 3 Store 4 70 60 180 150 Y-Coordinate 160 90 90 120 Formulate the NLP for this problem in which X and Y represent the X, Y coordinates of the new warehouse.
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- The distance between two cities in the United States can be approximated by the following formula, where lat1 and long1 are the latitude and longitude of city 1 and lat2 and long2 are the latitude and longitude of city 2. 69 (lat1 − lat2)2 + (long1 − long2)2 Ted's daughter is getting married, and he is inviting relatives from 15 different locations in the United States. The file Wedding gives the longitude, latitude, and number of relatives in each of the 15 locations. Ted would like to find a wedding location that minimizes the demand-weighted distance, where demand is the number of relatives at each location. Assuming that the wedding can occur anywhere, find the latitude and longitude of the optimal location. (Hint: Notice that all longitude values given for this problem are negative. Make sure that you do not check the option for Make Unconstrained Variables Non-Negative in Solver. Round your answers to three decimal places.) latitude of the optimal wedding location:…The Sunshine Rental Car Agency has six lots in Orlando,and it wants to have a certain number of cars available ateach lot at the beginning of each day for local rental. Theagency would like a model it could quickly solve atthe end of each day that would tell how to redistribute thecars among the six lots at the minimum total mileage.The distances between the six lots are as follows:In a 3 x 3 transportation problem, let xij be the amount shipped from source i to destination j and let cij be the corresponding transportation cost per unit. The amounts of supply at sources 1, 2, and 3 are 15, 30, and 85 units, respectively, and the demands at destinations 1, 2, and 3 are 20, 30, and 80 units, respectively. Assume that the starting northwest-corner solution is optimal and that the associated values of the multipliers are given us u1 = -2, u2 = 3, u3 = 5, v1 = 2, v2 = 5, and v3 = 10. a) Find the associated optimal cost. b) Determine the smallest value of cij for each nonbasic variable that will maintain the optimality of the northwest-corner solution.
- A coordinate system is superimposed on a map. Three existing facilities arelocated at (5, 15), (10, 20), and (6, 9). Compute both the rectilinear and theEuclidean distances separating each facility from a new facility located at (x, y) =(8, 8).Given the following existing facilities data: Existing facility #1 has weight 2 and coordinate (9, 10). Existing facility #2 has weight 10 and coordinate (6, 8). Existing facility #3 has weight 8 and coordinate (-3, -3). Existing facility #4 has weight 9 and coordinate (5, 2). Existing facility #5 has weight 3 and coordinate (-7, -1). Existing facility #6 has weight 7 and coordinate (-2, -6). Existing facility #7 has weight 4 and coordinate (-5, 0). Existing facility #8 has weight 3 and coordinate (4, -7). What is the optimal minisum rectilinear x-coordinate? What is the optimal minisum rectilinear y-coordinate? What is the optimal minisum rectilinear objective function value? Need allConsider 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 abov
- Find the indicated maximum or minimum value of the objective function in the linear programming problem. Minimize g = 10x + 6y subject to the following. x + 2y ≥ 10 2x + y ≥ 11 x + y ≥ 9 x ≥ 0, y ≥ 0A person starting in Columbus must visit Great Falls, Odessa, and Brownsville, and then return home to Columbus in one car trip. The road mileage between the cities is shown. Columbus Great Falls Odessa Brownsville Columbus --- 102 79 56 Great Falls 102 --- 47 69 Odessa 79 47 --- 72 Brownsville 56 69 72 --- a)Draw a weighted graph that represents this problem in the space below. Use the first letter of the city when labeling each b) Find the weight (distance) of the Hamiltonian circuit formed using the nearest neighbor algorithm. Give the vertices in the circuit in the order they are visited in the circuit as well as the total weight (distance) of the circuit.In the transportation model, you determine the lowest number first in the row then in the column & then subtract it to the numbers they are aligned in respectively. *FalseTrueThe transportation model is designed to maximize the total cost of delivering products from a source to a destination. *FalseTrueA goal programming problem had two equally important goals. Goal number 1: to achieve exactly $1,500 profit; Goal number 2: to avoid overtime. The objective function for this goal programming problem is written as: Minimize G = 2(d1-) + (d1+) + (d2+) *FalseTrueSetup cost (dollars per inventory unit per unit time) includes: capital invested in inventory, storage and handling of material, & insurance. *TrueFalsePlacing a new order whenever the inventory level drops to a specific re-order point is known as periodic order. *FalseTrue
- The management of Sunny Skies Unlimited now has decided that the decision regarding the locations of the paramedic stations should be based mainly on costs. The cost of locating a paramedic station in a tract is $200,000 for tract 1, $250,000 for tract 2, $400,000 for tract 3, $300,000 for tract 4, and $500,000 for tract 5. Management’s objective now is to determine which tracts should receive a station to minimize the total cost of stations while ensuring that each tract has at least one station close enough to respond to a medical emergency in no more than 15 minutes. In contrast to the origi- nal problem, note that the total number of paramedic stations is no longer fixed. Furthermore, if a tract without a station has more than one station within 15 minutes, it is no longer neces- sary to assign this tract to just one of these stations. Display and solve this model on a spreadsheet.A manufacturing company produces two types of products called X and Y. Each product uses four different machines like lathe, drilling, grinding & milling operations. The profit per unit of selling X and Y are 7 RO and 3 RO respectively. Formulate a linear programming model with the given constraints to determine the production volume of each product in order to maximize the total profit (in OR). Solve the following linear programming model by using Graphical method. Subject to, 6X + 4Y ≤ 24 X + 2Y ≤ 6 -X + Y ≤ 1 Y ≤ 2 and X,Y ≥ 0(a) Write the dual of the following linear programming problem: Maximize Ζ = 3x1 + 5x2 + 4x3, Subject to 2x1 + 3x2 ≤ 8, 2x2 + 5x3 ≤10 3x1 + 2x2 + 4x3 ≤15 x1 , x2 , x3 ≥ 0 (b) Find the optimal solution to the given problem in (a) above, using the simplex method. (c) From the final optimal table in (b) above, find the solution to the dual problem. (d) Give the economic interpretation to the solution in (c) above.