Linear programming model formulation. DataDecision variables Objectives Constraints 3. Coalco produces coal at three mines and ships it to four customers. The cost per ton ofproducing coal, the ash and sulfur content (per ton) of the coal, and the productioncapacity (in tons) for each mine are given in Table 1. The number of tons of coaldemanded by each customer is given in Table 2. The cost (in dollars) of shipping a ton ofcoal from a mine to each customer is given in Table 3. It is required that the total amountof coal shipped contains at most 5% ash and at most 4% sulfur.1Instructor: Lei ZhaoIntroduction to Decision MakingFall 2020Formulate a linear programming (LP) model that minimizes the cost of meeting customerdemands.Note: Clearly define your notation. You are NOT required to solve it.Table 1: Properties of coal from different minesProduction costСараcityAsh contentSulfur contentMine 1$501200.08ton0.05tonMine 2$551000.06ton0.04tonMine 3$621400.04ton0.03tonTable 2: Demand from each customerCustomer 1Customer 2Customer 3Customer 480706090Table 3: Cost (in dollars) from each mine to each customerCustomer 1Customer 2Customer 3Customer 4Mine 146.8.12Mine 29.6.711Mine 38123

Let Mi=Tons of coal produced at MineXi j =ton of coal shipped from mine i to customer jObjective…

. Coalco produces coal at three mines and ships it to four customers. The cost per ton of producing coal, the ash and sulfur content (per ton) of the coal, and the production capacity (in tons) for each mine are given in Table 1. The number of tons of coal demanded by each customer is given in Table 2. The cost (in dollars) of shipping a ton of coal from a mine to each customer is given in Table 3. It is required that the total amount of coal shipped contains at most 5% ash and at most 4% sulfur.

. Coalco produces coal at three mines and ships it to four customers. The cost per ton of producing coal, the ash and sulfur content (per ton) of the coal, and the production capacity (in tons) for each mine are given in Table 1. The number of tons of coal demanded by each customer is given in Table 2. The cost (in dollars) of shipping a ton of coal from a mine to each customer is given in Table 3. It is required that the total amount of coal shipped contains at most 5% ash and at most 4% sulfur.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section: Chapter Questions

Problem 61P

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