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Question;BUS;190;Homework 6 Solutions;1.;Tom's Inc. makes two salsa products: Western Foods salsa and Mexico City salsa.;Essentially, the two products have different blends of whole tomatoes, tomato;sauce, and tomato paste. A jar of Western Foods salsa uses 5 ounce of whole;tomatoes, 3 ounces of tomato sauce, and 2 ounces of tomato paste. A jar of;Mexico City salsa consists of 7 ounces of whole tomatoes, 1 ounce of tomato;sauce, and 2 ounces of tomato paste.;For the current production period Tom's Inc. can;purchase up to 4480 ounces of whole tomatoes, 2080 ounces of tomato sauce, and;1600 ounces of tomato paste. Tom?s Inc. makes a profit of $1.00 per jar of;Western Foods salsa and $1.25 per jar of Mexico City salsa.;The;following linear programming model was used to determine the mix of salsa products;that will maximize the total profit contribution.;W = Jars;of Western Foods Salsa;M = Jars of Mexico City;Salsa;Maximize 1W + 1.25M;Subject to;5W + 7M? 4480 (Whole tomatoes);3W + 1M? 2080 (Tomato sauce);2W + 2M? 1600 (Tomato paste);W,M? 0;The problem was;solved in Excel and the sensitivity report is shown on the next page.;Microsoft Excel;11.0 Sensitivity Report;Adjustable Cells;Final;Reduced;Objective;Allowable;Allowable;Cell;Name;Value;Cost;Coefficient;Increase;Decrease;$C$17;Western;Foods Salsa;560;0.000;1.00;0.107;0.25;$D$17 Mexico;City Salsa;240;0.000;1.25;0.25;0.15;Constraints;Final;Shadow;Constraint;Allowable;Allowable;Cell;Name;Value;Price;R.H. Side;Increase;Decrease;$K$10;Whole;Tomatoes;4480;0.125;4480;1120;160;$K$11;Tomato Sauce;1920;0.000;2080;1E+30;160;$K$12;Tomato Paste;1600;0.187;1600;40;320;a) What are the optimal production quantities?;b) What is the;profit of the optimal solution?;c) Which;constraints are binding?.;d);Which would be more valuable, an additional ounce of whole tomatoes or an;additional ounce of tomato paste?;e);How much less profit would Tom's make if they had 200 fewer ounces of tomato;sauce?;f);How would Tom?s profit change if they had 100 more ounces of whole tomatoes?;2.;Tri-County Utilities Inc. supplies natural gas to customers in a three county;area. The company purchases natural gas from two companies: Southern Gas and;Northwest Gas. Demand forecasts for the coming winter season are Hamilton;County, 400 units, Butler County, 200 units;and Clermont;County;300 units. Contracts to provide the following quantities have been written;Southern Gas, 500units, and Northwest Gas, 400;units. Distribution costs for the counties vary, depending upon thelocation;of the suppliers. The distribution costs per unit (in thousands of dollars) are;as follows;To;From;Hamilton;Butler;Clermont;Southern;Gas;10;20;15;Northwest;Gas;12;15;18;a) Draw a network representation of this;problem.;b);Formulate a transportation model;that can be used to determine the plan that will minimize total distribution;costs.;c);Use Excel to solve the problem.;State the optimal distribution plan and the total distribution costs. Please;turn in your spreadsheet as well.;Please see the spreadsheet online;for the model.;3. An air-conditioning manufacturer produces room;air conditioners at plants in Houston, Phoenix, and Memphis. These are sent to;regional distributors in Dallas, Atlanta, and Denver. The shipping costs vary;and the company would like to find the least-cost way to meet the demands at;each of the distribution centers.;Dallas;needs to receive 800 air-conditioners per month, Atlanta needs 600, and Denver;needs 200. Houston has 750 air-conditioners available each month, Phoenix has;550, and Memphis has 300.;The shipping;cost per unit from Houston to Dallas is $8, to Atlanta is $12, and to Denver is;$10. Due to truck capacity limits, no more than 50 air-conditioners can be;shipped between Houston and Denver each month.;The;cost per unit from Phoenix to Dallas is $10, and to Denver is $9. Air;conditioners from Phoenix are never shipped to Atlanta.;The;cost per unit from Memphis to Dallas is $11, to Atlanta is $8, and to Denver is;$12.;Formulate;a linear optimization model to determine how many units should be shipped from;each plant to each regional distribution center. You do not need to solve the;problem.;4.;Arnoff Enterprises manufactures the CPU for a line of computers. The CPUs are;manufactured in Seattle and Santa Clara and shipped to warehouses in;Pittsburgh, Mobile, Denver, Los Angeles, and Washington, D.C. The following;table shows the number of CPUs available at each plant, the number of CPUs;required by each warehouse, and the shipping costs (in dollars per CPU).;Warehouse;Plant;Pittsburgh;Mobile;Denver;Los;Washington;CPUs;Angeles;available;Seattle;10;20;5;9;10;9000;Santa;1;20;7;10;4;8000;Clara;CPUs;3000;5000;4000;6000;3000;required;(a) Draw a;network diagram of the problem.;(b);Are supply and demand equal to each other? No;(c);Formulate a linear optimization;model to determine the distribution plan that will minimize cost while meeting;as much demand as possible.;Since supply is less than;demand, we will need to include a dummy origin in our formulation with a;capacity of 4000 CPUs.;(d) Enter;the model in Excel. Please turn in your spreadsheet.;(e);Report the optimal solution and its cost.;(f) Which;if any, warehouses will have shortages and how big will the shortages be?


Paper#36521 | Written in 18-Jul-2015

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