Extra Practice - Sensitivity Analysis (Solutions).pptx - Real Estate Example 1 A real estate company wants to build and sell homes in a new development

Extra Practice - Sensitivity Analysis (Solutions).pptx -...

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Real Estate Example 1 A real estate company wants to build and sell homes in a new development. There will be three types of floor plans: Model I Model II and Model III. Each Model I will require 0.6 acres of land, each Model II will require 1 acre of land and each Model III will require 1.5 acres of land. Twelve acres of land are available. The company already has orders for three Model I and three Model II homes. They have also been told by the city to build not more than ten Model I homes. The company is restricted by availability of wood in that only 81 maple trees are available. Each Model I home requires 6 maple trees, each Model II house requires 9 maple trees and each Model II house requires 15 maple trees. The profit from a Model I home is $300,000,from a Model II home is $400,000 and from a Model III home is $420,000. How many of each type
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LP Formulation - Mathematical Decision variables x1 = number of Model I homes to build x2 = number of Model II homes to build x3 = number of Model III homes to build Objective Function Max z = 300,000 x1 + 400,000 x2 + 420,000 x3 Constraints  x1  x2  x3  12 (Land Availability) x1 > 3(Model I minimum) x2 > 3(Model II minimum) x1 < 10 (Model I maximum) x1  x2  x3  81 (Wood Availability) x1, x2, x3 0 (Non-negativity) 2
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Computer Sensitivity 3
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Impact of Possible Changes Change objective function coefficients Change RHS of existing constraints Adding/Removing a constraint Multiple changes 4
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Range of Optimality: Basic Variable 5 How does the optimal solution and the objective function value change if Profit of model 1 home increases to 400,000?
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