Concept explainers
Explanation of Solution
Given:
Let
Writing the matrix of basic variables and
Writing the B matrix,
Compute the
Writing
Find the coefficient of
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- Andalus Furniture Company has two manufacturing plants, one at Aynor and another at Spartanburg. The cost in dollars of producing a kitchen chair at each of the two plants is given here. Aynor: Cost = 65Q1 + 5Q12 + 96Spartanburg: Cost = 21Q2 + 3Q22 + 147 Where Q1 = number of chairs produced at Aynor Q2= number of chairs produced at Spartanburg Andalus needs to manufacture a total of 50 kitchen chairs to meet an order just received. How many chairs should be made at Aynor and how many should be made at Spartanburg in order to minimize total production cost? Can you use Excel to formulate and Solver to solve.arrow_forward20. What do you mean by optimal solution?arrow_forwardConsider the following LP and its optimal tableau: max z = 3x1 + 2x2s.t. 2x1 + 5x2 ≤ 8 3x1 + 7x2 ≤ 10 x1, x2 ≥ 0 a) Find the dual of this LP and its optimal solution. b) Find the range of values of b2 for which the current basis remains optimal. Also find the new optimal solution if b2 = 5.arrow_forward
- Portfolio manager Max Gaines needs to develop an investment portfolio for his clients who are willing to accept a moderate amount of risk. His task is to determine the proportion of the portfolio to invest in each of the five mutual funds listed below so that the portfolio maximizes the expected return but provides an annual return of no less than 3%. for each of the following scenarios. Annual Returns (Planning Scenarios): mutual fund yr 1 yr 2 yr 3 yr 4 international stock 22.37 26.73 6.46 -3.19 low-cap blend 14.88 18.61 10.52 5.25 mid-cap blend 19.45 18.04 5.91 -1.94 small-cap blend 13.79 11.33 -2.07 6.85 intermediate bond 7.29 8.05 9.18 3.92 Formulate the appropriate linear program for this situation. (state the objective function, the decision variables, and the constraints)arrow_forwardQuestion 31 An optimal solution is only optimal with respect to a particular mathematical model that provides only a representation of the actual problem. O True O Falsearrow_forwardThe following LP formulation represents a transportation problem where raw material (in tons] from Supplier i, i={1,2,3} to Plant j, j={1,2,3). The problem is solved and the optimal objective function value is 5200. Using the sensitivity report shown below, what would be the optimal total cost if the cost of transporting 1 ton from Supplier 1 to Plant 1 becomes 2 and the cost of transporting 1 ton from Supplier 3 to Plant 3 becomes 2.5? Min Total cost = 1x11 + 3x12 + 5x13 +3.5x21 +4x22+4.8x23 +3.5x31+3.6x32+3.2x33 Subject to x31+x32+x33 = 0, for i= {1,2,3} &j= {1, 2, 3} Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease Name 500 1 2.5 1E+30 700 3 0.6 1E+30 200 1E+30 0.2 0 2.5 0 1E+30 1E+30 0.2 1E+30 1 1E+30 200 2.5 0 1E+30 0.6 1.8 1E+30 Variables X11 X12 X13 X21 X22 X23 X31 X32 X33 10 200 000000000 5 3.5 4 4.8 3.5 3.6 3.2arrow_forward
- K = 0, L = 18 Write and solve the following linear program using lingo, take screen shots of your model as well as the reports and the optimal solution. Clearly show the optimal solution.NB:K=the second digit of your student number;L=sum of the digits of your student number, For example if your student number is 17400159 thenK=7andL=1+7+4+0+0+1+5+9=27!!!! SAVE YOUR FILE BY YOUR STUDENT NUMBER!!!!minz=t∈T∑(AtYt+PtXt)+k∈K∑(HkUk+BkVk)s.t.Uk+Vk=50∀k∈KXt−CtYt<=0∀t∈Tk∈K∑Vk≥80t∈T∑Xt≥t∈T∑DtXt>=0∀t∈TYt∈{0,1}∀t∈TUk>=0∀k∈KVk>=0∀k∈KThe sets parameters and data are as follows: \[ \begin{array}{l} \mathrm{T}=\{1,2,3,4\} \\ \mathrm{K}=\{0,1,2,3,4\} \\ \mathrm{A}=\{5000,7000,8000,4000\} \\ \mathrm{D}=\{250,65,500,400\} \\ \mathrm{C}=\{500,900,700,800\} \\ \mathrm{P}=\{20, \mathrm{~L}, 25,20\} \\ \mathrm{H}=\{5,3,2, \mathrm{~K}, 9\} \\ \mathrm{B}=\{8,5,4,7,6\} \end{array} \]arrow_forwardA construction company has four large bulldozers located at four different garages. The bulldozers are to be moved to four different construction sites. The distances in miles between the bulldozers and the construction sites are given below. Bulldozer/ A B C D Site Students 1 90 75 75 80 solve it 2 35 85 55 65 yourself 3 125 95 90 105 4 45 110 95 115 How should the bulldozers be moved to the construction sites in order to minimize the total distance traveled?arrow_forwardCan someone give an example/explanation of reading the optimal substructure from given code? I.e you're given a bit of code and then you have to determine what the optimal substructure is.arrow_forward
- Please use the Hungarian Method for finding the optimal assignment of jobs to workers. Abigail charges 12 dollars for Yardwork, 25 dollars for Repairs, and 20 dollars for Painting.Bich charges 3 dollars for Yardwork, 5 dollars for Repairs, and 16 dollars for Painting.Caleb charges 4 dollars for Yardwork, 10 dollars for Repairs, and 18 dollars for Painting.You want all three jobs done for the cheapest total amount possible between these three workers.arrow_forwardFinish the computation of the following main table of constructing an optimal BST and write down the process in detail. Thank youarrow_forwardSuppose the risk index for the stock fund (the value of ) increases from its current value of 8 to 12. How does the optimal solution change, if at all? Suppose the risk index for the money market fund (the value of ) increases from its current value of 3 to 3.5. How does the optimal solution change, if at all? Suppose increases to 12 and increases to 3.5. How does the optimal solution change, if at all?arrow_forward
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole