1 In the Dakota problem, show that the current basis remains optimal if c3, the price of chairs, satisfies 15 < Cz < 22.5. If c3 = 21, find the new optimal solution. Also, if c3 25, find the new optimal solution.
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- SO what would be the L, Lq, and Wq of this problem? Assuming we are trying to develop and sovle a waiting line system that can accomodate this increased leel of passenger traffic.Are you able to use complementary slackness and your answer to part (a) to find solution(s) to the primal LPP? Why or why not?answer to part (a): attached here No, it does not have an optimal solution.In a binary model which schedules a fire crew, the modeler wishes to impose the restriction that if employee B is selected to work on the shift, neither employee D nor employee E can be selected. How is this constraint to be written? Question 14 options: xD + xE + xB = 1 xD + xE + 2xB < 2 xD + xE - 2xB < 1 xD + xE + 2xB < 1 xD + xE + xB > 1
- Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance contract for its new computerized wheel alignment and balancing machine. Managers feel that maintenance expense is related to usage of the machine, and they have collected the following information on weekly usage of the machine (in hours) and annual maintenance expense (in hundreds of dollars) from 10 other companies that own the machine.Company Weekly Usage(hours) Annual maintenance Expense(hundreds of dollars)A 13 17.0B 10 22.0C 20 30.0D 28 37.0E 32 47.0F 17…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?Consider the equality-constrained linear program: minimize cT x subject to Ax = b. Show that if A has full column rank and b ∈ range(A), then this problem always has a unique bounded solution, regardless of the definition of c. Do Lagrange multipliers exist? If they exist, are they unique?
- An engineer is studying the mileage performance characteristics of 5 types of gasoline additives. In the road test he wishes to use cars as blocks; however, because of a time constraint, he must use an incomplete block design. He runs the balanced design with the five blocks that follow. Car Additive 1 2 3 4 5 1 NA 17 14 13 12 2 14 14 NA 13 10 3 12 NA 13 12 9 4 13 11 11 12 NA 5 11 12 10 NA 8 - Verify that this is a balanced incomplete block design - Obtain the estimates of the treatment means and the treatments effectsPart A: “Infeasibility means that no solution to the LPP satisfies all the constraints, including the non-negativity restrictions.” Discuss on the above statement.Mo. For each of the following shaded region in Figure 1, can it be the feasible region of a linear program?
- Consider the given graph below. The weights represent the time, in minutes of reaching one destination from another destination. Using the Brute Force Method in this complete weighted graph, determine all the Hamilton circuits starting at L and its optimal solution.Write down the mathematical expressions for: The market-clearing condition when all endowments are owned by a private-sector individual and that an allocation (x, y) must be feasible in a world with private-endowment, but NO production.22) Determine using the Simplex algorithm the optimal solution to the following linear programming problem: