Consider the following problem.Maximize Z = 20x₁ + c₂x₂,subject to 3x₁ + a₁₂x₂ ≥ 60 5x₂ + a₂₂x₂ ≤ 100 and x₁ ≥ 0,x₂ ≥ 0,where x₁ represents the level of activity 1 and x₂ represents the level of activity 2.The values of c₂,a₁₂,and a₂₂ have not been determined yet.Only activity 1 needs to be undertaken soon whereas activity 2 will be initiated somewhat later.There are two different,but equally likely,scenarios that could unfold between now and the time activity 2 is undertaken that would lead to different values for c₂,a₁₂,and a₂₂,as listed below.Scenario 1: c₂ = 30,a₁₂= 4,and a₂₂ = 7 Scenario 2: c₂ = 10,a₁₂ = 1,and a₂₂ = 3 The goal is to use all of this information to choose a value for x₁ now and to simultaneously determine a plan for choosing a value of x₂ later after seeing which scenario has occurred.Use stochastic programming with recourse to formulate the appropriate model for this problem.

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The Answer of Consider the following problem.Maximize Z = 20x₁ + c₂x₂,subject to 3x₁ + a₁₂x₂ ≥ 60 5x₂ + a₂₂x₂ ≤ 100 and x₁ ≥ 0,x₂ ≥ 0,where x₁ represents the level of activity 1 and x₂ represents the level of activity 2.The values of c₂,a₁₂,and a₂₂ have not been determined yet.Only activity 1 needs to be undertaken soon whereas activity 2 will be initiated somewhat later.There are two different,but equally likely,scenarios that could unfold between now and the time activity 2 is undertaken that would lead to different values for c₂,a₁₂,and a₂₂,as listed below.Scenario 1: c₂ = 30,a₁₂= 4,and a₂₂ = 7 Scenario 2: c₂ = 10,a₁₂ = 1,and a₂₂ = 3 The goal is to use all of this information to choose a value for x₁ now and to simultaneously determine a plan for choosing a value of x₂ later after seeing which scenario has occurred.Use stochastic programming with recourse to formulate the appropriate model for this problem.

Consider the Following Problem