This Solved Assignment covers key management concepts in MGT 420. Download now!
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MGT 420ASSIGNMENT 11.Logan, Ltd. makes two products, tables and chairs, which must be processed through assembly andfinishing departments. Each table requires5hours to assemble and3hours to finish, but each chairrequires2hours to assemble and5hours to finish. Assembly department has80 hours available, andfinishing department can handle up to90 hours of work. The company wants to see at least5chairsproduced during the production.The production of chairsshould be more than or equal tothe productionof tables.Each table yields a profit of $8, and each chair can be sold for a profit of $4.a. Show the feasible regiongraphically (Draw a graph by using MS WORD).b. What are the extreme points of the feasible region?c. Find the optimal solution using the graphical method.d. Are there any slack values? Are there any surplus values?e. Compute the shadow pricesofeachconstraint.Answer:Problem Breakdown:Logan, Ltd. produces two products—tables and chairs. We need to determine the number of tables (T) andchairs(C) to produce to maximize profit while considering various constraints. Here's the information provided:•Time requirements for processing:oTables: 5 hours to assemble, 3 hours to finishoChairs: 2 hours to assemble, 5 hours to finish•Available time:oAssembly department: 80 hoursoFinishing department: 90 hours•Profit:oProfit per table = $8oProfit per chair = $4•Constraints:oAt least 5 chairs should be produced: C≥5C\geq 5oThe number of chairs produced should be greater than or equal to the number of tables: C≥TC\geq ToTime constraints:▪5T + 2C ≤ 80 (Assembly department constraint)▪3T + 5C ≤ 90 (Finishing department constraint)a. Feasible Region Graphically:To create the graph, plot the inequalities on a graph. Use the following steps:1.Graph theassembly constraint: 5T+2C≤805T + 2C\leq 80oRewrite for CC: C=80−5T2C =\frac{80-5T}{2}2.Graph the finishing constraint: 3T+5C≤903T + 5C\leq 90oRewrite for CC: C=90−3T5C =\frac{90-3T}{5}3.Add the other constraints:oC≥5C\geq 5oC≥TC\geq T4.Plot the feasible region formed by these inequalities.You can use MS Word or Excel to plot these graphs. The feasible region will be the area bounded by the lines ofthese inequalities.b. Extreme Points of the Feasible Region:To determine the extreme points of the feasible region, solve the system of equations formed by the intersection ofthe boundary lines of the constraints. The extreme points represent potential solutions. These points are where theconstraints intersect.The system of equations that we need to solve to find the intersections is:1.5T+2C=805T + 2C = 80 (Assembly constraint)
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