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 Customer D 1 1 D 2 2 D 3 3 D 4 4 Clifton Springs 1 $32 $34 $32 $40 Danville 2 $34 $30 $28 $38 The plant capacities and customer orders are as follows Plant Capacity (units) Clifton Springs 5,000 Danville 3,000 Distributor Orders (units) D 1 2,000 D 2 5,000 D 3 3,000 D 4 2,000 (a)How many units should each plant produce for each customer to maximize profits Units Cost Clifton Springs D 1 $ Clifton Springs D 2 $ Clifton Springs D 3 $ Clifton Springs D 4 $ Danville D 1 $ Danville D 2 $ Danville D 3 $ Danville D 4 $ Total Cost $ (b)Which customer demands will not be met Distributor 1 will have a shortfall of units Distributor 2 will have a shortfall of units Distributor 3 will have a shortfall of units Distributor 4 will have a shortfall of units (c)Show your network model and linear programming formulation (i)network model (Submit a file with a maximum size of1 MB ) This answer has not been graded yet (ii)linear programming formulationLet x ij 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 $$32 X 11 34 X 12 32 X 13 40 X 14 34 X 21 30 X 22 28 X 23 38 X 24 s t Orders from Clifton Springs 1 x 11 1 x 12 1 x 13 1 x 145000 Orders from Danville 1 x 21 1 x 22 1 x 23 1 x 243000 Orders from for Dummy Node $$ x 11 x 212000 Orders for D 1 Orders for D 2 Orders for D 3 Orders for D 4 x ij 0 for all i , j JUST NEED ANSWERS FOR ORDERS FOR D1 D4 Optimal Solution

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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

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	Customer
D₁ 1	D₂ 2	D₃ 3	D₄ 4
Clifton Springs 1	$32	$34	$32	$40
Danville 2	$34	$30	$28	$38

The plant capacities and customer orders are as follows.

Plant	Capacity (units)
Clifton Springs	5,000
Danville	3,000

Distributor Orders (units)
D₁	2,000
D₂	5,000
D₃	3,000
D₄	2,000

(a)How many units should each plant produce for each customer to maximize profits?

	Units	Cost
Clifton Springs-D₁		$
Clifton Springs-D₂		$
Clifton Springs-D₃		$
Clifton Springs-D₄		$
Danville-D₁		$
Danville-D₂		$
Danville-D₃		$
Danville-D₄		$
Total Cost		$

(b)Which customer demands will not be met?Distributor 1 will have a shortfall of units.Distributor 2 will have a shortfall of units.Distributor 3 will have a shortfall of units.Distributor 4 will have a shortfall of units.(c)Show your network model and linear programming formulation.(i)network model (Submit a file with a maximum size of1 MB.)

This answer has not been graded yet.

(ii)linear programming formulationLetx_ij= number of unitsishipped to clientj, 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

$$32X11+34X12+32X13+40X14+34X21+30X22+28X23+38X24

s.t.Orders from Clifton Springs

1x11+1x12+1x13+1x145000

Orders from Danville

1x21+1x22+1x23+1x243000

Orders from/for Dummy Node

$$x11+x212000

Orders forD₁

Orders forD₂

Orders forD₃

Orders forD₄

x_ij0 for alli,j.