Use the BIP branch-and-bound algorithm to solve the following problem. Using Breadth first left as a branching approach. Minimize Z= 5x + 6x + 7x3 + 8x,+9xs, subject to 3x - x2 + x+ x-2rs 2 2 x+3x-x- 2x + x 20 -X - + 3x + x+ x2 1 and x, is binary, for j= 1, 2,....5.
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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.)Implement and explain all the steps of the Branch and Bound method for the following optimization problem: max 15x1 + 12x2 + 4x3 + 2x4s.t. 8x1 + 5x2 + 3x3 + 2x4 ≤103x1 + 2x3 ≤4x1, x2, x3, x4 binaryWe illustrated how a machine replacement problem can be modeled as a shortest path problem. This is probably not the approach most people would think of when they first see a machine replacement problem. In fact, most people would probably never think in terms of a network. How would you model the problem? Does your approach result in an LP model?
- 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…Explain all the steps when implementing the Branch and Bound method for the following optimization problem: Max 15*x1+12*x2+4*x3+2*x4 s.t. 8*x1+5*x2+3*x3+2*x4 <=10 3*x1+2*x3<=4 x1, x2, x3, x4 binarySolve the following problems using Excel Solver or R Studio. A company produces cars in Atlanta, Boston, Chicago, and Los Angeles. The cars are then shipped to warehouses in Memphis,Milwaukee, New York City, Denver, and San Francisco. The number of cars available at each plant is given in Table 1. Eachwarehouse needs to have available the number of cars given in Table 2. The distance (in miles) between the cities is given inTable 3. Assuming that the cost (in dollars) of shipping a car equals the distance between two cities, determine an optimalshipping schedule.
- A company has four warehouses and six stores. The warehouses altogether have a surplus of 22 units of a given commodity, divided among them as follows: Warehouses 1 2 3 4 Surplus 5 6 2 9 The six stores altogether need 22 units of the commodity. Individual requirements at b stores 1,2,3,4,5 and 6 are 4,4,6,2,4 and 2 units respectively. Cost of shipping one unit of commodity from warehouse i to store j in $ dollars is given in the matrix below. Stores Warehouses 1 2 3 4 5 6 1 9 12 9 6 9 10 2 7 3 7 7 5 5 3 6 5 9 11 3 11 4 6 8 11 2 2 10 Required Formulate the mathematical model for the problem How should the products be shipped from the warehouses to the stores so that the transportation cost is minimum?Please solve the following problem as a linear program. My diet requires that all the food I eat come from one of the four “basic food groups” (chocolate cake, ice cream, soda, and cheesecake). At present, the following four foods are available for consumption: brownies, chocolate ice cream, cola, and pineapple cheesecake.Each brownie costs 50¢, each scoop of chocolate ice cream costs 20¢, each bottle of cola costs 30¢, and each piece of pineapple cheesecake costs 80¢. Each day, I must ingest at least 500 calories, 6 oz of chocolate, 10 oz of sugar, and 8 oz of fat. The nutritional content per unit of each food is shown in the following table. Formulate a linear programming model that can be used to satisfy my daily nutritional requirements at minimum cost.What is linear programming? Give an example of an application of linear programming
- 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:…An Insurance Company is introducing two new product lines: special risk insuranceand mortgages. The expected profit is $5 per unit on special risk insurance and $2 per unit onmortgages. Management wishes to establish sales quotas for the new product lines tomaximize total expected profit. Please see figure for work requirements(a) Formulate a linear programming model for this problem.A firm has 4 plants that produce widgets. Plants A, B, and C can each produce 100 widgets per day. Plant D can produce 50 widgets per day. Each day, the widgets produced in the plants must be shipped to satisfy the demand of 3 customers. Customer 1 requires 75 units per day, customer 2 requires 100 units per day, and customer 3 requires 175 units per day. The shipping costs for each possible route are shown in the table below: Shipping Costs Customer per unit Plant 1 2 3 A $ 25 $ 35 $ 15 B $ 20 $ 30 $ 40 C $ 40 $ 35 $ 20 D $ 15 $ 20 $ 25 The firm needs to satisfy all demand each day, but would like to minimize the total costs. The firm’s problem falls within which classification? Multiple Choice Cost-benefit-trade-off Assignment problems Transshipment problems Transportation problems Resource-allocation