X,Y 20 1.) Plot and label the constraints C₁, C₂ and C3 (using the line drawing tool) on the provided graph. 2.) Using the point drawing tool, plot the point that maximizes the objective function. The optimum solution is: x=(round your response to two decimal places). Y= (round your response to two decimal places). Optimal solution value Z = (round your response to two decimal places).
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- b) 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?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…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
- 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…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 ≥ 0We have 60 meters of fence and want to fence a triangular shaped area. Please formulate an NLP (do not try to solve) that will enable us to maximize the fenced area (Hint: The area of a triangle with sides of length a, b, and c is ( s (s – a) (s – b) (s – c))1/2, where s is half the parameter of the triangle).
- Chapter 6. Solve the following Linear Program using the Solver method and answer the questions given below (round to two decimal places): Maximize 12A + 15B s.t. 3A + 7B <= 250 5A + 2B <= 200 B <= 25 A, B >= 0 a. The optimal value of A is 31.03 and the optimal value of B is 22.41. b. The maximized function yields a solution of 708.62. Chapter 7. For the problem you solved in Q1, obtain the Sensitivity Report, and answer the following questions. Remember to round to two digits and you can enter “infinity” for unlimited regions: The range for Variable A is from ????? to ????? The range for Variable B is from ????? to ????? The range for Constraint 1 is from ????? to ????? The range for Constraint 2 is from ????? to ????? The range for Constraint 3 is from ????? to ?????Simplex Method Solve the following LP problem using the simplex method. Maximize: P = 9x + 7ySubject to:2x + y ≤ 40x + 3y ≤ 30x, y ≥ 0 What is the entering variable and leaving variable in Table 2? a. Entering Variable: x and Leaving Variable: S2 b. Entering Variable: y and Leaving Variable: S2 c. Entering Variable: y and Leaving Variable: S1 d. Entering Variable: x and Leaving Variable: S1Set 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 .
- INCORRECT FORFormulate a linear programming model that can be used to determine the pounds of Brazilian Natural and Colombian Mild that will maximize the total contribution to profit. (Let BR = pounds of Brazilian beans purchased to produce Regular, BD = pounds of Brazilian beans purchased to produce DeCaf, CR = pounds of Colombian beans purchased to produce Regular, and CD = pounds of Colombian beans purchased to produce DeCaf.) Max 2.033BR+2.582BD+1.868CR+2.418CD INCORRECT Pounds of Regular BR+CR≤900 INCORRECT Pounds of DeCaf BD+CD≤400 INCORRECTAnalyze algebraically what special case in simplex application is present in each of the LP model below. Give an explanation to support your answer. a) Maximize z = 4x1 + 2x2 Subject to: 2x1 - x2 ≤ 2 3x1 - 4x2 ≤ 8 x1, x2 ≥ 0b) Maximize z = 3x1 + 2x2 Subject to: 4x1 - x2 ≤ 8 4x1 + 3x2 ≤ 12 4x1 + x2 ≤ 8 x1, x2 ≥ 0Indetify the constraints that form the fesible region and identify the constraints that are rebundant. Equation: Maximize 5x1 + 3x2 Subjected to x1 + 5x2 ≤ 5 4x1 + 3x2 ≤ 12 x1 + x2 ≤ 4 x1 + x2 ≤ 5 5x1 + 7x2 ≤ 35 x1 + x2 ≥ 0