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I need answers for all five questions A technology company manufactures smartphones, tablets, laptops, and smartwatches. The manufacturing process involves different resources such as electronic
I need answers for all five questions
A technology company manufactures smartphones, tablets, laptops, and smartwatches. The manufacturing process involves different resources such as electronic components, assembly labor, and quality testing. The company also needs to adhere to supply contracts with two major distributors. They decided to use a Linear Programming (LP) model to optimize their production plan. LP Formulation: 1- Decision Variables: x1 : Number of smartphones produced. x2 : Number of tablets produced. x3 : Number of laptops produced. x4 : Number of smartwatches produced. 2- Objective Function: Maximize z=40x1+30x2+50x3+20x4 3- Constraints: Subject to: 4x1+3x2+5x3+2x41500(Electroniccomponentsconstraint)3x1+4x2+2x3+x41000(Assemblylaborconstraint)2x1+2x2+3x3+3x41200(Qualitytestingconstraint)2x1+3x2+x3+2x4700(DistributorAcontract)x1+x2+2x3+x4500(DistributorBcontract)x1,x2,x3,x40(Non-negativityconstraints) The nrohlem is solved using the Big-M Method (M=100) and the optimal tableau is given below: 3-Constraints: Subject to: 4x1+3x2+5x3+2x41500(Electroniccomponentsconstraint)3x1+4x2+2x3+x41000(Assemblylaborconstraint)2x1+2x2+3x3+3x41200(Qualitytestingconstraint)2x1+3x2+x3+2x4700(DistributorAcontract)x1+x2+2x3+x4500(DistributorBcontract)x1,x2,x3,x40(Non-negativityconstraints) The problem is solved using the Big-M Method (M=100) and the optimal tableau is given below: Where s1,s2, and s3 are the slacks for the Electronic components, Assembly labor, and Quality testing constraints, respectively. While s4 and s5 are the surplus variables for the Distributor A and Distributor B contracts, respectively. Based on the given formulation and the given optimal tableau, you are required to prepare a detailed report to answer the following questions: 1. Is the obtained solution a unique optimal solution (YES/NO)? Why? 2. Identify which of the five constraints is binding and which is non-binding, showing how you recognize the constraint state. 3. Find the dual price for each of the five constraints. 4. Find the feasibility range for each dual price. 5. Find the optimality range for each coefficient in the objective function. NOTE: The final answers to the above requirements are given in the next page. Dual prices and feasibility range for each constraint are as followsStep by Step Solution
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