Hello! I'm having trouble with this practiceproblem. I'm not too sure why it's coming back as incorrect on thelatter half.
Hello I M Having Trouble With This Practice Problem I M Not Too Sure Why It S Coming Back As Incorrect On The Latter H 1 (34.05 KiB) Viewed 59 times
Hello I M Having Trouble With This Practice Problem I M Not Too Sure Why It S Coming Back As Incorrect On The Latter H 2 (31.9 KiB) Viewed 59 times
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. Plant Clifton Springs Danville Plant 1 Clifton Springs Danville L2 D $32 D₂ D3 Customer $34 $30 5,000 $34 $32 The plant capacities and customer orders are as follows. Capacity (units) 3,000 $28 3 4 D4 $40 $38 Distributor Orders (units) D₁ D₂ D3 D₂ 2,000 5,000 3,000 2,000
(a) How many units should each plant produce for each customer to maximize profits? Optimal Solution Clifton Springs-D₁ 0 Clifton Springs-D₂ 4000 Clifton Springs-D3 Clifton Springs-D4 1000 Danville-D₁ Danville-D₂ Danville-D3 Danville-D4 Total Cost 0 2000 0 0 1000 Units S (b) Which customer demands will not be met? Distributor 1 will have a shortfall of 0 Distributor 2 will have a shortfall of 1000 Distributor 3 will have a shortfall of 3000 Distributor 4 will have a shortfall of 0 $0 $136000 $0 $ 40000 $ 68000 $0 $0 Cost $38000 $282000 units. units. units. units.
(ii) linear programming formulation Let Xij = number of units i shipped to client j, using the indices from the given table. (It may be necessary to combine plants or distributors in a single node in order to solve this problem. Use index number 5 for this type of node. Enter "DNE" in any unused answer blanks.) Max 32x13 +34x₁4+32x15 s.t. +40x16 +34x23 X₁, ≥ 0 for all i, j. +30x24 Orders from Clifton Springs X13X14X15 +*16= 5000 Orders from Danville X23 +X24+x25 +*26 = 3000 Orders from/for Dummy Node X73 +X74 +X75 +X76= 4000 Orders for D₁ X13 +*23 +X73=2000 Orders for D₂ X14+x24+x74= 5000 Orders for D₂ X15+X25+X75 = 3000 Orders for D4 X16 +x26 +x76=2000 X X X + 28x25 X X X +38x20 X
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