Find the optimal solution to this linear programming problem
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| Max | 2X + 3Y | ||||
| s.t. | |||||
| 4X + 9Y | ≤ | 71 | |||
| 10X + 11Y | ≤ | 111 | |||
| 17X − 9Y | ≤ | 152 | |||
| X, Y ≥ 0 |
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- Sometimes we wish to analyze the effect of changing a parameter over a wide range of values. Performing changes over a wide range is known as parametric analysis. This can be accomplished by using the sensitivity analysis to establish the range above and below the current value, and then changing the current value to a number outside the current range to find a new range for this parameter. For example, consider the following model: minimize 5X1 + 8X2 subject to (1) 2X1 + 5X2 ≥ 910 (2) 4X1 + 3X2 ≥ 1092 (3) X1 + 9X2 ≥ 819 X1 , X2 ≥ 0 (a) Solve this model graphically. (b) From the graph, perform a sensitivity analysis on b2, the rhsUse the simplex method to solve. Maximize z = 4x1 + 2x2, subject to 3x1 + x2 < 22 3x1 + 4x2 < 34 x1 > 0, x2 > 0 x1 = x2 = x3 =a wine maker has a stock of three different wines with the following characteristics Wine proofs acids(%) specific gravity stock(gallons) A 27 .32 1.70 20 B 33 .20 1.08 34 C 32 .30 1.04 22 A dry table wine should be between 30 and 31 degree proof, it should contain at least 0.25% acid and should have a specific gravity of at least 1.06. The wine maker wishes to blend the three types of wine to produce as large a quantity as possible of satisfactory dry table wine. However, his stock of wine A must be completely used in the blend because further storage would cause it to deteriorate. What quantities of wines of B and C should be made in the blend. Formulate this problem as LP model. a wine maker has a stock of three different wines with the following characteristicsWine proofs acids(%) specific gravity stock(gallons)A 27 .32 1.70 20B 33 .20 1.08 34C 32 .30 1.04 22 A dry table wine…
- Consider the following all-integer linear program:max 5x1 + 8x2s.t. 9x1 + 4x2 ≤ 361x1 + 2x2 ≤ 10x1, x2 ≥ 0 and integer.The equation below specifies a function with independent variable x. Determine whether the function is linear, constant, or neither x=2y+5Solve by the Big M – method: Maximize Ζ= x1 + 2x2 −3x3 + x4 Subject to x1 +2x2 +3x3 =15 2x1 +x2 + 5x3 = 20 x1 +2x2 +x3 +x4 = 10 x1 + 4x2 +6x3 ≤ 5 Where x x x x1, 2, 3, 4 ≥ 0
- Set up the simplex matrix used to solve the linear programming problem. Assume all variables are nonnegative. Maximize f = 8x + 9y + 3z subject to 2x + 7y + 8z ≤ 100 6x + 3y + z ≤ 160 3x + 4y + 9z ≤ 10 .Consider the following LP problem developed at Zafar Malik's Carbondale, Illinois, optical scanning firm: Maximize Z= 1X1+1X2 Subject to: 2X1+1X2≤72 (C1) 1X1+2X2≤72 (C2) X1,X2≥0The values of the same 15 student in two subject A and B are given below the two numbers within the brackets denoting the ranks of the same student in A and B respectively.(1,10), (2,7), (3,2), (4,6), (5,4), (6,8), (7,3), (8,1), (9,11),(10,15), (11,9), (12, 5), (13, 14), (14,12), (15, 13). Find the rank correlation coefficient.
- Is my solution correct and did I fully answer the questions? (see attachment for my solution) Question: There are three factories on Momiss River. Each emits two types of pollutants, labeled P1 and P2, into the river. If the waste from each factory is processed, the pollution in the river can be reduced. It costs $1,500 to process a ton of factory 1 waste, and each ton processed reduces the amount of P1 by 0.10 ton and the amount of P2 by 0.45 ton. It costs $2,500 to process a ton of factory 2 waste, and each ton processed reduces the amount of P1 by 0.20 ton and the amount of P2 by 0.25 ton. It costs $3,000 to process a ton of factory 3 waste, and each ton processed reduces the amount of P1 by 0.40 ton and the amount of P2 by 0.50 ton. The state wants to reduce the amount of P1 in the river by at least 125 tons and the amount of P2 by at least 175 tons. a. Use Solver to determine how to minimize the cost of reducing pollution by the desired amounts. Are the LP assumptions…Solve Maximize: Z = 4X1 + 3X2 + 9X3 Subject to: 2X1 + 4X2 + 6X3 ≥ 15 6X1 + X2 + 6X3 ≥ 12 X1, X2, X3 ≥ 0 Use simplex method.Please help with correct answers in details: step by step Q1 The optimal solution of this linear programming problem is at the intersection of constraints 1 and 2. Max 3x1 + x2 s.t. 4x1 + x2 ≤ 400 4x1 + 3x2 ≤ 600 x1 + 2x2 ≤ 300 x1, x2 ≥ 0 Over what range can the coefficient of x1 vary before the current solution is no longer optimal? (Round your answers to two decimal places.) ______ to ______? Over what range can the coefficient of x2 vary before the current solution is no longer optimal? (Round your answers to two decimal places.) _______ to _______? Compute the dual value for the first constraint. _______ Compute the dual value for the second constraint. _______ Compute the dual value for the third constraint. _______