Solve the following goal programming model graphically and by using the computer: minimize Pīd† , Pzdz , P3dž subject to 4x1 + 2x2 + dĩ - dị = 80 x1 + d, - dž = 30 x2 + d, – dž = 50 Li d d 2 0
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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.)Given this linear programming model, solve the model and then answer the questions that follow. Maximize Z = 12x1 + 18x2 + 15x3 where x1 = the quantity of product 1 to make, etc. Subject to Machine: 5x 1 + 4x 2 + 3x 3 ≤ 160 minutes Labor: 4x1 + 10x2 + 4x3 ≤ 288 hours Materials: 2x 1 + 2x2 + 4x3 ≤ 200 pounds Product 2: x2 ≤ 16 units x1, x2, x3 ≥ 0 a) Are any constraints binding? If so, which one(s)? b) If the profit on product 3 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain. c) If the profit on product 1 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain. d) If 10 hours less of labor time were available, what would the values of the decision variables be? The objective function? Explain. e) If the manager decided that as many as 20 units of product 2 could be produced (instead of 16), how much additional profit would be generated? f) If profit per unit on each…Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Minimize C = 17x + 19y subject to 8x + 14y ≥ 21 11x + 6y ≥ 31 and x ≥ 0, y ≥ 0. What is the optimal value of x and y? What is the minimum value of the objective function? Please show me step by step how to do this by hand, not through excel.
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- 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?An enterprise produces P1, P2 and P3 products using H1 and H2 raw materials. Production data are presented in the table below. The labor time per unit of P1 product is twice that of P2 and three times that of P3. The entire workforce of the production facility is enough to produce 1500 units of P1 product. The market requirement for products is in the order of 3: 2: 5. Establish the Linear programming (DP) model that will maximize the profits of the business and determine the best production quantities?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: ______________________________________________________________
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