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You are the recently hired Chief Operations Officer at ABC Inc

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Question;(20 pts.)You are;the recently hired Chief Operations Officer at ABC Inc, a regional firm;which produces specialized circuit boards used in the production of;various makes and models of automobiles.;The company currently owns three production plants, one much newer;than the other two. Once the;circuit boards are produced, the firm ships them to one of four warehouses;throughout the state where they are placed in inventory until ordered by;the end-user. Each circuit board;sells for $150.;Being the good COO that you;are, you are always looking for ways to minimize costs and increase;profitability. You suspect that there is;much room for improvement in this regard.;Specifically, you have reason to believe that production and stocking;levels of each plant and warehouse could be modified to yield the desired;results.;The details of this managerial;challenge are as follows;Production Costs - Plant;A -- $100 per circuit board;Plant;B -- $120 per circuit board;Plant;C -- $90 per circuit board;Plant;Capacity - Plant A ? 1,200 circuit boards;Plant B ? 1,200 circuit boards;Plant C ? 500 circuit boards;Demand Forecast - Warehouse;#1 ? 700 circuit boards;Warehouse #2 ? 400 circuit boards;Warehouse #3 ? 600 circuit boards;Warehouse #4 ? 500 circuit boards;Shipping Costs;Warehouse #1;Warehouse #2;Warehouse #3;Warehouse #4;Plant A;$10;$15;$40;$30;Plant B;$50;$20;$25;$20;Plant C;$25;$45;$30;$22;Create a linear program that;shows exactly how many circuit boards should be produced at each plant and then;shipped to each warehouse in order to maximize resulting profits. Your completed model should show the optimal;values of all 12 decision variables AS WELL AS the optimal value of the;objective function.;(20 pts.) Given the following LP model;Minimize;(costs) Z = 4X1 + 8X2;Subject;to Fiber 5X1 + 8X2 > 40;Protein 6X1 + 4X2 > 24;X1, X2 > 0;a.) What is the optimal value of the objective;function?;b.) What are the optimal values of the two;decision variables?;c.) Find the range of optimality for each;objective function coefficient.;d.) How would a decrease of $1 in the X1;coefficient of the objective function affect the optimal values of the decision;variables?;e.) How would a decrease of $1 in the X1;coefficient of the objective function affect the optimal value of the objective;function?;f.) What is the dual value (AKA ??shadow;price?) for the RHS of the protein constraint?;g.) What is the range of feasibility of the;dual value for the RHS of the protein constraint?;h.) What impact on total cost would a decrease;of 2 units in the RHS of the protein constraint have? Please explain the rationale for your answer.;3. (20 pts.);The manager of FYZ Incorporated has been presented with the;following LP model;Minimize (costs) Z = 30A + 45B;Subject;to 5A + 2B >;100;4A;+ 8B > 240;B > 20;A;and B > 0;She;would like your assistance with several questions below.;a.) What is the proper name of the last;constraint shown in the model?;b.) What is the optimal value of the objective;function?;c.) What are the optimal values of the two;decision variables?;d.) If the cost of B could be reduced to $42;per unit, how many units of B would be optimal?;e.) If the cost of B could be reduced to $42;per unit, what would the minimum total cost be?;f.) What is the dual value (AKA--?shadow;price?) for the RHS value of the first constraint?;g.) What is the range of feasibility for the;RHS value of the first constraint?;By what amount;would the total cost change, and in what direction, if the RHS value of the;first constraint was changed to 110?;Please explain the rationale for your answer.

 

Paper#60444 | Written in 18-Jul-2015

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