5. Use Dual Simplex method to solve the LPP. Min. Z = 3W₁ + 4W2 Subject to where 3W1 +4W2 ≥ 24 2W₁ +W₂ ≥ 10 5W₁+ 3W2 ≥ 29 W₁, W₂ ≥ 0
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- Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. Letting R = number of regular gloves C = number of catcher's mitts leads to the following formulation: Max 5R + 8C s.t. R + 3 2 C ≤ 800 Cutting and sewing 1 2 R + 1 3 C ≤ 240 Finishing 1 8 R + 1 4 C ≤ 100 Packaging and shipping R, C ≥ 0 The computer solution is shown below. Optimal Objective Value = 3520.00000 Variable Value Reduced Cost R 320.00000 0.00000 C 240.00000 0.00000 Constraint Slack/Surplus Dual Value 1 120.00000 0.00000 2 0.00000 3.00000 3 0.00000 28.00000 Variable ObjectiveCoefficient AllowableIncrease AllowableDecrease R 5.00000 7.00000 1.00000 C 8.00000 2.00000 4.66667 Constraint RHSValue AllowableIncrease AllowableDecrease 1 800.00000 Infinite 120.00000 2 240.00000 160.00000 106.66667 3…Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. Letting R = number of regular gloves C = number of catcher's mitts leads to the following formulation: Max 6R + 9C s.t. R + 3 2 C ≤ 1,000 Cutting and sewing 1 2 R + 1 3 C ≤ 300 Finishing 1 8 R + 1 4 C ≤ 100 Packaging and shipping R, C ≥ 0 The computer solution is shown below. Optimal Objective Value = 4350.00000 Variable Value Reduced Cost R 500.00000 0.00000 C 150.00000 0.00000 Constraint Slack/Surplus Dual Value 1 275.00000 0.00000 2 0.00000 4.50000 3 0.00000 30.00000 Variable ObjectiveCoefficient AllowableIncrease AllowableDecrease R 6.00000 7.50000 1.50000 C 9.00000 3.00000 5.00000 Constraint RHSValue AllowableIncrease AllowableDecrease 1 1000.00000 Infinite 275.00000 2 300.00000 100.00000 166.66667 3…Don't use chatgpt, I will 5 upvotes Alan wants to bake blueberry muffins and bran muffins for the school bake sale. For a tray of blueberry muffins, Alan uses 1/3 cup of oil and 2 eggs. For a tray of bran muffins, Alan uses 1/2 cup of oil and 1 egg. Alan has 4 cups of oil and 12 eggs on hand. He sells trays of blueberry muffins for $12 each and trays of bran muffins for $9 each. Alan wants to maximize the money raised at the bake sale. Let x represent the number of blueberry muffins and y represent the number of bran muffins Alan bakes.
- b) Consider the LP below:Solve using the big M- methodMinimize Z = 20X1 + 10X2s.t X1 + 2X2 ≤ 403X1 + X2 ≥ 304X1 + 3X2 ≥ 60X1, X2, ≥ 0Consider the following LP problem: Min 6X+ 27Y Subject to : 2 X + 9Y => 25, and X + Y <= 75. Pick a suitable statement for this problem: a. X=37.5, Y=37.5 is the only optimal solution. b. Optimal Obj. function value is 75 c. X = 0, Y = 0 is the only optimal solution. d. Optimal Obj. function value is 0Simplex Method Solve the following LP problem using the simplex method. Maximize: P = 9x + 7ySubject to:2x + y ≤ 40 x + 3y ≤ 30x, y ≥ 0 What is the entering variable and leaving variable in Table 1? Choices: A. Entering Variable: y and Leaving Variable: S1 B. Entering Variable: x and Leaving Variable: S1 C. Entering Variable: x and Leaving Variable: S2 D. Entering Variable: y and Leaving Variable: S2
- Find solution using BigM (penalty) method.Maximize Z = x1 + 2x2 + 3x3 - x4subject to the constraintsx1 + 2x2 + 3x3 = 152x1 + x2 + 5x3 = 20x1 + 2x2 + x3 + x4 = 10and x1, x2, x3, x4 ≥ 04 Sunco processes oil into aviation fuel and heating oil. Itcosts $40 to purchase each 1,000 barrels of oil, which isthen distilled and yields 500 barrels of aviation fuel and 500barrels of heating oil. Output from the distillation may besold directly or processed in the catalytic cracker. If soldafter distillation without further processing, aviation fuelsells for $60 per 1,000 barrels, and heating oil sells for $40per 1,000 barrels. It takes 1 hour to process 1,000 barrels ofaviation fuel in the catalytic cracker, and these 1,000 barrelscan be sold for $130. It takes 45 minutes to process 1,000barrels of heating oil in the cracker, and these 1,000 barrelscan be sold for $90. Each day, at most 20,000 barrels of oilcan be purchased, and 8 hours of cracker time are available.Formulate an LP to maximize Sunco’s profits.22. Suppose that the feasible region of a maximization LP problem has corners of (0,0), (10,0), (5,5), and (0,7). If profit is given to be $X + $3Y what is the maximum profit the company can earn? Part 2 A. $10 B. $0 C. $14 D. $21 E. $15
- Optimal solution 4T+3C=240 2T+1C=100 →T=30, C-40 Can you please explain to me the solution and way of how he did get the exact coordinate points in the graph? I know there is a formula or way to calculate since it is hard to find out the exact point when manually plotting a graphSolve this using Simplex method Maximize: 4x1 + 2x2 + 5x3 S.t. x1 + 2x2 + x3 <=25 x1 + 4x2 + 2x3<=40 3x1 + 3x2 + x3 <= 30 x1, x2, x3>=0b) Maximize Z = −40X1 −100X2s.t 10X1 + 5X2 ≤ 2502X1 + 5X2 ≤ 1002X1 + 3X2 ≤ 90X1, X2 ≥ 0Solve by simplex method, what are the solutions? Show that this problem hasmultiple solutions and find the solutions?