Find the optimal level of production for the following minimization problem using graphical linear programming method. use the following information Minimization function is Z=8x1+12x2 Subject to: 5x1+2x2≥20 4x1+3x2≥24 X2≥2
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- Solve Problem 1 with the extra assumption that the investments can be grouped naturally as follows: 14, 58, 912, 1316, and 1720. a. Find the optimal investments when at most one investment from each group can be selected. b. Find the optimal investments when at least one investment from each group must be selected. (If the budget isnt large enough to permit this, increase the budget to a larger value.)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 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.)
- Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Minimize C = 14x + 7y + 8z subject to 6x + 12y + 19z ≥ 64 17x + 24y + 9z ≥ 128 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?Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Minimize C = 8x + 8y subject to 7x + 9y ≥ 16 10x + 10y ≥ 22 and x ≥ 0, y ≥ 0. What is the optimal value of x? What is the optimal value of y? What is the minimum value of the objective function?Solve these problems using graphical linear programming and answer the questions that follow. Usesimultaneous equations to determine the optimal values of the decision variables.a. Maximize Z = 4x1 + 3x2Subject toMaterial 6x1 + 4x2 ≤ 48 lbLabor 4x1 + 8x2 ≤ 80 hrx1, x2 ≥ 0 b. Maximize Z = 2x1 + 10x2Subject toDurability 10x1 + 4x2 ≥ 40 wkStrength 1x1 + 6x2 ≥ 24 psi Time 1x1 + 2x2 ≤ 14 hrx1, x2 ≥ 0 c. Maximize Z = 6A + 3B (revenue)Subject toMaterial 20A+ 6B ≤ 600 lbMachinery 25A+ 20B ≤ 1,000 hr Labor 20A+ 30B ≤ 1,200 hrA, B ≥ 0 (1) What are the optimal values of the decision variables and Z?
- 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?Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.) Maximize p = x + 2y subject to x + 5y ≤ 6 4x + y ≤ 5 x ≥ 0, y ≥ 0. p= (x, y)=Consider the following linear programming problem: MIN Z = 3x1 + 2x2 Subject to: 2x1 + 3x2 ≥ 12 5x1 + 8x2 ≥ 37 x1, x2 ≥ 0 What is minimum cost and the value of x1 and x2 at the optimal solution?
- Consider the following set of constraints: -4X <= -512; -28Y <= -3584; 0.5 X + 14Y >= 1792, and 2X + 2Y <= 256. Pick a right statement for this problem: a. Feasible region is represented by a line and multiple feasible points are available. b. The feasible region is defined by a single (unique) point. c. Feasible region does not exist. d. All the options are incorrect. e. Solution to this problem cannot be found without the objective functionSolve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.) Minimize c = x + 2y subject to x + 3y ≥ 23 8x + y ≥ 23 x≥ 0, y≥ 0. c= x,y=Consider the following linear programming model with 4 regular constraints:Maximize 3X + 5Y (a) Draw your graph in the space below:subject to: 4X + 4Y ≤ 48 (constraint #1) 4X + 3Y ≤ 50 (constraint #2) 2X + 1Y ≤ 20 (constraint #3) X ≥ 2 (constraint #4) X, Y ≥ 0 (non-negativity constraints)(a) Which of the constraints is redundant? Constraint #______.Justify by drawing a graph similar to Figure 7.14 on p.263.(b) Is point (9,3) a feasible solution? _____. Explain your answer (by analyzing each of the constraints).Constraint #1: _______________________________________________________________Constraint #2: _______________________________________________________________Constraint #3: _______________________________________________________________Constraint #4: ______________________________________________________________