The point (4, 5) is feasible for the constraint 2x₁ + 6x₂ ≤ 30. O True O False
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- 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).4. 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.One constraint of a two decision variable LP problem is 3x+ 4y ≤ 2400. The point (300, 400), that is x = 300 and y = 400 is _________. a. a solution with regard to 3x + 4y ≤ 2400 b. a corner point of the feasible region c. not a solution with regards to 3x + 4y ≤ 2400 d. a point on the line of constraint 3x+ 4y ≤ 2400
- Find the indicated maximum or minimum value of the objective function in the linear programming problem. Minimize g = 10x + 6y subject to the following. x + 2y ≥ 10 2x + y ≥ 11 x + y ≥ 9 x ≥ 0, y ≥ 0Find the values of x1 and x2 where the following two constraints intersect. (Round your answers to 3 decimal places.) (1) 10x1 + 5x2 ≥ 50 (2) 1x1 + 2x2 ≥ 12The 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.
- Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Maximize C = 14x + 13y + 5z subject to 9x + 11y + 18z ≤ 61 14x + 15y + 12z ≤ 122 and x ≥ 0, y ≥ 0, z ≥ 0. What is the optimal value of x? What is the optimal value of y? What is the optimal value of z? What is the maximum value of the objective function?The constraint 5x 1 − 2x 2 ≤ 0 passes through the point (20, 50). True FalseFind the optimal solution for the following problem. (Round your answers to 3 decimal places.) Minimize C = 11x + 5y + 10z subject to 8x + 12y + 19z ≥ 68 13x + 16y + 5z ≥ 136 and x ≥ 0, y ≥ 0, z ≥ 0. What is the optimal value of x? What is the optimal value of y? What is the optimal value of z? What is the minimum value of the objective function?
- Set up the simplex matrix used to solve the linear programming problem. Assume all variables are nonnegative.Maximize f = 5x + 9y subject to 8x + 5y ≤ 200 x + 6y ≤ 250. x y s1 s2 f first constraint second constraint objective functionFind the optimal solution for the following problem. Maximize C = 4x + 12y subject to 3x + 5y ≤ 12 6x + 2y ≤ 10 and x ≥ 0, y ≥ 0. What is the optimal value of x? What is the optimal value of y? (Round your answer to 3 decimal places.) What is the maximum value of the objective function? (Round your answer to 3 decimal places.)Consider the following linear programming problem: Min Z = 50x1 + 60x2 s.t. 6x1 + 5x2 >= 30 8x1+4x2 >= 32 x1,x2 >=0. What is the Z in the optimal point of this problem? a. 200 b. 250 c. 300 d. 350 e. none of the abov