# The number of hours consultant campbell assigned to

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= the number of hours consultant Campbell assigned to client Ax32= the number of hours consultant Campbell assigned to client Bx33= the number of hours consultant Campbell assigned to client Cx34= the number of hours consultant Campbell assigned to client DMaximize C = 100x11+ 125x12+ 115x13+ 100x14+ 120x21+ 135x22+ 115x23+ 120x24+ 155x31+ 150x32+140x33+ 130x34s.t.x11+ x12+ x13+ x14≤ 160x21+ x22+ x23+ x24≤ 160x31+ x32+ x33+ x34≤ 140x11+ x21+ x31= 180x12+ x22+ x32= 75x13+ x23+ x33= 100x14+ x24+ x34= 85xij≥ 0,i,j6Klein Chemicals, Inc., produces a special oil-based material that is currently in short supply. Four of Klein’scustomers have already placed orders that together exceed the combined capacity of Klein’s two plants. Klein’smanagement faces the problem of deciding how many units it should supply to each customer. Because thefour customers are in different industries, different prices can be charged because of the various industrypricing structures. However, slightly different production costs at the two plants and varying transportation costsbetween the plants and customers make a “sell to the highest bidder”strategy unacceptable. After consideringprice, production costs, and transportation costs, Klein established the following profit per unit for each plant–customer alternative:The plant capacities and customer orders are as follows:Show your network model and linear programming formulation.Tri N Anthony Situmorang
Let:x11= the number of units produced by Clifton Springs for customer D1x12= the number of units produced by Clifton Springs for customer D2x13= the number of units produced by Clifton Springs for customer D3x14= the number of units produced by Clifton Springs for customer D4x21= the number of units produced by Danville for customer D1x22= the number of units produced by Danville for customer D2x23= the number of units produced by Danville for customer D3x24= the number of units produced by Danville for customer D4Maximize C = 32x11+ 34x12+ 32x13+ 40x14+ 34x21+ 30x22+ 28x23+ 38x24s.t.x11+ x12+ x13+ x14= 5000x21+ x22+ x23+ x24= 3000x11+ x21≤ 2000x12+ x22≤ 5000x13+ x23≤ 3000x14+ x24≤ 2000xij≥ 0,i,jThe problem can also be modeled using dummy origin so that the number of supply equals the number ofdemand, making the demand constraints be all equations instead inequalities (less than or equal to). Thenumber of units distributed from the dummy origin represents the unsatisfied demand.Tri N Anthony Situmorang

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The Dummy, Clifton Springs New York, Anthony Situmorang
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