a) State whether the following are true or false. i) In an LP problem, at least one corner point must be an optimal solution if an optimal solution exists. ii) In an assignment problem, it may be necessary to add more than one row to the data. iii) In the shortest route technique, the objective is to determine the route from an origin to a destination that passes through the fewest number of other nodes.
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- Prove that if a canonical LP problem has two optimal solutions then it has an infinite number of optimal solutions.An unmanned rover must be routed to visit four sites labeled A, B, C, and D on the surface of the moon. Table 6-7 shows the distance (in kilometers) between any two sites. Assuming the rover landed at C, find an optimal tour. An unmanned rover must be routed to visit four sites labeled A, B, C, and D on the surface of the moon. Table 6-7 shows the distance (in kilometers) between any two sites. Assuming the rover landed at C, find an optimal tour.Scott and Associates, Inc., is an accounting firm that has three new clients. Project leaders will be assigned to the three clients. Based on the different backgrounds and experiences of the leaders, the various leader–client assignments differ in terms of projected completion times. The possible assignments and the estimated completion times in days are as follows: Requireda. Develop a network representation of this problem.b. Find the optimal solution using the Hungarian method. What is the total time required?
- It has been said that each LP problem that has a feasible region has an infinite number of solutions. Explain.Give the corners of the feasible set and the maximum and minimal value.A shop has four machinists to be assigned to four machines. The hourly cost of having each machine operated by each machinist is as follows: However, because he does not have enough experience, machinist 3 cannot operate machine B. a. Determine the optimal assignment and compute total minimum cost. b. Formulate this problem as a general linear programming model.
- we will be looking at the travels of a fictional circus with just a single touring unit. This Atlanta-based circus plans to visit 24 cities, listed in the table below. After visiting all of the cities, the circus will return to Atlanta. The goal of the circus is to find a good tour of all the cities; that is, to find a path that visits each city and then returns to its starting point. Of course, some tours are shorter than others, and the optimal tour is the one which covers the least total distance. Atlanta, GA Detroit, MI Lincoln, NE Phoenix, AZ Boston, MA Indianapolis, IN Minneapolis, MN Pittsburgh, PA Buffalo, NY Jacksonville, FL Nashville, TN Portland, OR Charlotte, NC Kansas City, MO New Orleans, LA Salt Lake City, UT Chicago, IL Las Vegas, NV Oakland, CA San Antonio, TX Cleveland, OH Lexington, KY Oklahoma City, OK San Diego, CA The raw city-to-city distance data (HW2data.xls) can be found in an Excel spreadsheet on Canvas. All distances are symmetric; the distance from city A…Graph the following solution set, and determine the feasible region in graph. Also determine corresponding control points of the bounded region.