Operation Research Midterm

Solve the sideline problem graphically (Please be neat). Draw the polytope on the x-y coordinate system ( tush be done either by hand or computer). Show all intersection of the polytope and identify the point (x,y coordinate) where the objective function is maximized and provide that value. Maximize Z = 31 + 22 Subject to 11 + 12 ? 10 81 + 12 ? 24 and x1, x2 ? 0 consequence Point (a) is the origin (0,0) where Z(a) = 3*0 + 2*0 = 0Point (b) is the intersection of line 2 and X-axis (3,0) where Z(b) = 3*3 + 2*0 = 9 Point (c) is the intersection of line 1 and line 2 (2,8) where Z(c) = 3*2 + 2*8=22 . (Optimum Solution) Point (d) is the intersection of line 1 and Y-axis (0,10) where Z(d) = 3*0 + 2*10 = 20 Y X d a b c I II puzzle 5. (30 Points) Work through the simplex method (in algebraic form) step by step to solve the following problem. Show all work and provide the solutions for severally variable at every iteration of the simplex.Maximize z = 41 + 32 + 43 Subject to 21 + 22 + 13 ? 20 21 + 12 + 23 ? 14 11 + 12 + 33 ? 15 and x1, x2, x3 ? 0 Solution Problem 6. (30 Points) The Weigelt Corporation has three branch plants with scanty harvest-homeion capacity. Fortunately, the corporation has a new product ready to begin production, and all three plants have this capability, so some of the excess capacity can be used in this way. This product can be made in three sizeslarge, medium, and lilliputianthat yield a net unit profit of $420, $360, and $300, respectively.Plants 1, 2, and 3 have the excess capacity to bring out 750, 900, and 450 units per day of this product, respectively, regardless of the size or combination of sizes involved. The amount of available in-process fund space overly imposes a limitation on the production rates of the new product. Plants 1, 2, and 3 have 13,000, 12,000, and 5,000 upstanding feet, respectively, of in-process storage space available for a days production of this product. Each unit of the large, medium, and small sizes pro duced per day requires 20, 15, and 12 square feet, respectively.Sales forecasts indicate that if available, 900, 1,200, and 750 units of the large, medium, and small sizes, respectively, would be sold per day. At each plant, some employees will need to be laid off unless most of the plants excess production capacity can be used to produce the new product. To avoid layoffs if possible, management has decided that the plants should use the same percentage of their excess capacity to produce the new product. Management wishes to know how much of each of the sizes should be produced by each of the plants to maximize profit. 1. Formulate a linear programming model for this problem by A.Listing and labeling all of the ratiocination variables. B. Creating an objective function for the model. C. List all of the constraints for the model. I want a complete model, not equitable an Excel sheet. 2. Solve the model using Excel solver or Open Office Solver. lend oneself the value for each deci sion variable and the objective function.