Question

The last questions choices are customer 1,customer 2, customer 3, customer 4 demand has a shortfall of  2000,4000,6000,8000,10000

customer 1, customer 2, customer 3, customer 4 demand of 2000,4000,6000,8000,10000

Klein Chemicals, Inc., produces a special oil-based material that is currently in short supply, Four of Klein's customers have already placed orders that together exceed the combined capacity of Klein's two plants. Klein's management faces the problem of deciding how many units it should supply to each customer. Because the four customers are in different industries, different prices can be charged because of the various industry pricing structures. However slightly different production costs at the two plants and varying transportation costs between the plants and customers make a "sell to the highest bidder strategy unacceptable. After considering price, production costs, and transportation costs, Klein established the following profit per unit for each plant-customer alternative: D1 $96 $102 D3 D4 $120 5114 Clifton Springs 596 $102 590 The plant capacities and customer orders are as follows Distributor Orders (units) Di 4000 D2 10000 D36000 Plant Capacity (units) Clifton Springs 10000 6000 How many units should each plant produce for each customer in order to maximize profits? Which customer demands will not be met? Choose correct network model and Show linear programming formulation. If the constant is 1 it must be entered in the box. If your answer is zero, enter Note: Dummy origin has supply of 8000. (iv) D1 D1 102 102 C.S. C.S. D2 10000 10000 102 114 D3 6000 D3 6000 8000 Dummy 8000 Dummy D4 D4 Let x = amount of units produced by plant node i for customer node). x12 13 X23 s.t. Xi2 X13 r14 0 for all i, j Cost, $ Units Clifton Springs D1 Clifton Springs D2 Clifton Springs D3 Clifton Springs D,4 Danville D1 Danville D2 Danville -D3 Danville -D Dummy D1 Dummy D2 Dummy D3 Dummy D4 Total Cost demand has a shortfall of Customer1 demand of is not satisfied

Answer 1

68x21 56 Vx23 10,000 6,000 1x4 8,000Dummy 1x21+ 1x23 1x31+ 1x32 1x33+ 1x11 1 V x12 xj 2.0 for all ,j

P Q C D EF GH I JK L M N x11 x12 x13x14 x21 x22x23 x24 x31 x32 x33 x34 2 Value of Profit 64 68 64 80 68 60 56 76 0 0 0 0 SUMPRODUCT(SC$3:SN$3,C4:N4) 4 -SUMPRODUCT(SC$3:SNS3,C6N6) 10000 -SUMPRODUCT(SC$3:SNS3,C7N7)6000 1111SUMPRODUCT SC$3 SN$3,C8:N8) 8000 -SUMPRODUCT(SCS3:SNS3,C9 N9)4000 -SUMPRODUCT(SC$3:SNS3,C10:N10) 10000 -SUMPRODUCT(SC$3:SNS3,C1N11) 6000 1 SUMPRODUCT SC$3:SNS3,C12:N12)- 4000 Capacity-2 Capacity-3 Demand-1 1 Demand-2 Demand-3 Demand-4 9 10 12

Set Objective OMin OY O Max Value Of: By Changing Variable Cells: $C$3:SN$3 Subject to the Constraints: Add Change Delete Reset All Load/Save Make Unconstrained Variables Non-Negative Select a Solving Method Simplex LP Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help Solve Close

Solution

	Units	Profit
Clifton Springs - D1	0	0
Clifton Springs - D2	8000	544000
Clifton Springs - D3	0	0
Clifton Springs - D4	2000	160000
Danville - D1	4000	272000
Danville - D2	0	0
Danville - D3	0	0
Danville - D4	2000	152000
Dummy - D1	0	0
Dummy - D2	2000	0
Dummy - D3	6000	0
Dummy - D4	0	0
Total		1128000

Customer 2demand has a shortfall of 2000. Customer 3 demand of 6,000 is not satisfied.

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