Q3:A/ Find the solution to the following linear programming problem by dual simplex method Min Z= 2X₁+4X₂ Subjected to: 2X₁-4X₂+2X3 ≥8 4X₁+2X₂-2X3 ≥ 12 X1, X2, X3 20
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- Please show how to solve b?Q-Find the solution by using the simplex method MAX Z= 2X1+3X2+X3 - :S. T X1+6X2+X3 ≤ 6 X1+2X2+X3 ≤ 4 X1-X2+X3 ≤ 3 X1, X2,X3 ≥ 0Q2. Solve the given LP problem on the right by (LP): Max Z = 2X1 + 4X2 %3D using The Graphical Solution Method. a) Find the optimal solution, determine the solution type. b) Find the optimality range for the changes in the objective coefficient c2. c) Find the feasibility range for the changes in the Right Hand Side (RHS) of one st. 3X1 + 2X2 < 12 Xị + 2X2 s 8 2X1 + X2 2 2 X1, X2 2 0 of the binding constraints.
- Briefly explain these terms:a. Basic variableb. Shadow pricec. Range of feasibilityd. Range of optimality3) Maximize Z= 2x, +x2 +3x 3 X+x2+2x3 <25 + X3 5 8 X2+ x3 S10 X1, X2, X3 2 0 Subject to IMe3 II | Here are the changes to the original problem and the revised conditions for this decision-making problem: With a favorable market, John Thompson thinks a large facility would result in a net profit of $195,000 to his firm. If the market is unfavorable, the construction of a large facility would result in $185,000 net loss. A small plant would result in a net profit of $110,000 in a favorable market, but a net loss of $25,000 would occur if the market was unfavorable. Doing nothing would result in $0 profit in either market conditions. a) Create a decision table, b) What is your recommendation if you would apply the Maximax criterion (Optimistic)? Follow the guidance from your textbook and create a table. c) What is your recommendation if you would apply the Maximin Criterion (Pessimistic)? Follow the guidance from your textbook and create a table. d) What is your recommendation if you would apply the Criterion of Realism (Hurwicz Criterion) with a coefficient of realism a =…
- Maximize Profit=123 L + 136 S 17 L+11 S≤ 3000 6 L+9 S≤2500 L20 and S20 (Availability of component A) (Availability of component B) Show Transcribed Text Implement the linear optimization model and find an optimal solution. Interpret the optimal solution. The optimal solution is to produce LaserStop models and SpeedBuster models. This solution gives the possible profit, which is $. (Type integers or decimals rounded to two decimal places as needed.)1 2-Binomial Coefficients: Problem 8 (1 point) What is the coefficient of ¹¹ in the expansion of (x + 2)¹2+x²¹(x+3) ²²?Q4) A rural country administration wants to locate several medical emergency response units so that it can respond to calls within the county within eight minutes of the call. The county is divided into seven population zones. The distance between the centers of each pair of zones is known and is given in the matrix below. The response units can be located in the center of population zones 1 through 7 at a cost (in hundreds of thousands of dollars) of 100, 80, 120 110, 90, 90, and 110 respectively. Assuming the average travel speed during an emergency to be 60 miles per hour, formulate an appropriate set covering model to determine where the units are to be located and how the population zones are to be covered.
- Next question Use the simplex method to solve the linear programming prob z= 8x1 - 7x2 + 4x3 2x1 Maximize X2 + 8x3 s 40 4x1 - 5x2 + 6x3576 2x1 - 2x2 + 6x3< 32 X120, X2 20, хз 20. subject to Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The maximum is , X2 =, X3 = S2 = and s3 when X1 S1 = B. There is no maximum.Maximize 8x + 9y Subject to -- x + 2 y 0 a) Solve using simplex methodSolve the following decision tree using the EMV rule and state the optimal strategy. B C .25 D 35 E 40 F 2 G 8 20 -50 H J K M N R 180 50 S 55 T 45 U 25 V 35 W S X 5 Y 4 Z 6 AA 3 BB 4 CC 3 300 100 10 80 -30 120 500 --200 150 100 50