x1 + x2 ≤30 300 ≤5x1 + 6x2 x1 ≥0, x2 ≥0. From the given constraint above, provide the following a. label the curves b. give the point of intersection of the constraints c. indetify the feasible regions
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x1 + x2 ≤30
300 ≤5x1 + 6x2
x1 ≥0, x2 ≥0.
From the given constraint above, provide the following
a. label the
b. give the point of intersection of the constraints
c. indetify the feasible regions
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- Consider the following LP:Maximize z = 16x1 + 15x2subject to40x1 + 31x2 <=124-x1 + x2<= 1x1<=3x1, x2 >= 0(a) Solve the problem by the simplex method, where the entering variable is thenonbasic variable with the most negative z-row coefficient.Indetify 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 ≥ 0Consider the given LP:Maximize z = 4x1 + 6x2 + 8x3Subject to 3x1 + 2x2 + 5x3<= 30 9x1 + 2x2 + 7x3 <= 126 2x1 + 3x2 + x3<= 60 xi>= 01-Find the optimal values of Z, x1, x2, x3 by using the simplex method.3-If the RHS of the constraint 1 is 34 instead of 30, what is the new value of Z?
- A chemical company must produce exactly 1,000 kilograms of a special mixture of phosphate and potassium for a customer. The phosphate costs $5 per kilogram and potassium costs $6 per kilogram. No more than 300 kilograms of phosphate can be used, and at least 150 kilograms of potassium must be used. The problem is to determine the least-cost blend of the two ingredients. Restate the problem mathematically by: a) Showing the decision variablesb) Showing the objective functionc) Showing the constraintsd) Solve the linear programming problem by graphingIn preparing a ≥ constraint for an initial simplex tableau, you would a. add a surplus variable. b. add slack variable. c. subtract an artificial variable. d. subtract a surplus variable and add an artificial variable.Consider the following LP model in standard form, with a row for the objective function Z. a) Put it into Canonical form ( or Simplex Tableau form) with basic variables X1, X2 , and X3. b) Determine the association BFS (Basic Feasible Solution) and the new formula for the objective function Z Minimize 10X1 + 4X2 Sujbject to 3X1 + 2X2 - X3 = 60 7X1 + 2X2 - X4 = 84 3X1 + 6X2 -X5 = 72 X1, X2, X3 , X4 , X5 >= 0
- Consider the following problem: Minimize Z = 5X1 + 8X2 + 3X3 + 5X4 + 12X5 Subject to X1 + 3X2 + 5X3 + 6X4 + 3X5 > 60 and all variables are > 0, except X1 which is of unrestricted sign Use the Primal-Dual relations to solve both problems (i.e., the Primal and the Dual).We 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).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?
- Let A = {0, 1, 2, 3} and define a relation R on A as follows: R = {(0, 0), (0, 2), (0, 3), (2, 2), (2, 0), (1, 1), (2, 1), (3, 3)}. (a) Draw the directed graph of R. (b) Is R reflexive? Explain. (c) Is R symmetric? Explain. (d) Is R transitive? Explain4. Consider the following linear programming problem: Maximize Z=$15x + $5y, subject to (1) 2x + y ≤ 10 and (2) 4x + 3y ≤ 24 and (3) x, y ≥ 0. Will the optimal solution change if the objective function becomes Maximize Z=$15x + $20y (constraints remain the same)? Select one: a. Can't determine given the information. b. Yes, it will change. c. No, it remains the same.The standard form of the following linear programming model is given. Find the values of variables at the point of intersection of constraint 1 and the vertical axis (y). (Round your answers to 3 decimal places.) Maximize P = 30x + 15y + 0s1 + 0s2 subject to 6x + 12y + s1 = 19 13x + 12y + s2 = 35 and x, y, s1, s2≥ 0.