Operation Research Midterm

Solve the following task graphic onlyy (Please be neat). Draw the polytope on the x-y coordinate system (can 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 look upon. maximize Z = 31 + 22 Subject to 11 + 12 ? 10 81 + 12 ? 24 and x1, x2 ? 0 Solution Point (a) is the origin (0,0) where Z(a) = 3*0 + 2*0 = 0Point (b) is the intersection of concern 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 fuss 5. (30 Points) Work finished the simplex method (in algebraic form) step by step to form the following problem. Show all work and provide the solutions for each multivariate 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 tether branch plants with excess work capacity. Fortunately, the corporation has a new product ready to begin production, and all three plants shake this capability, so some of the excess capacity can be utilize in this way. This product can be made in three coatslarge, medium, and smallthat yield a net unit profit of $420, $360, and $300, respectively.Plants 1, 2, and 3 have the excess capacity to micturate 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 storage space as well as imposes a limitation on the production rates of the new product. Plants 1, 2, and 3 have 13,000, 12,000, and 5,000 square feet, respectively, of in-process storage space available for a days production of this product. Each unit of the large, medium, and small sizes produced p er day requires 20, 15, and 12 square feet, respectively.Sales forecasts intimate 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 allow 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 theatrical role of their excess capacity to produce the new product. Management wishes to know how practically 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 determination variables. B. Creating an objective function for the model. C. List all of the constraints for the model. I want a complete model, not just an Excel sheet. 2. Solve the model using Excel solver or Open Office Solver. Give the value for each decision variable and the objective function.