7 Problem 6 06 PLEASE ANSWER USING THE FORMAT BELOW TO AVOID CONFUSION OR ELSE, I MIGHT DOWNVOTE THANK YOU Klein Chemicals, Inc , produces a special oil based material that is currently in short supply Four of Kleins customers have already placed orders that together exceed the combined capacity of Klein's two plants Kleins 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 plantcustomer alternative Customer Plant D 1 D 2 D 3 D 4 Clifton Springs $32 $34 $32 $40 Danville $34 $30 $28 $38 The plant capacities and customer orders are as follows Plant Capacity (units) Distributor Orders (units) Clifton Springs 5000 D 1 2000 D 2 5000 Danville 3000 D 3 3000 D 4 2000 How many units should each plant produce for each customer in order to maximize profits Which customer demands will not be met Show linear programming formulation If the constant is 1 it must be entered in the box If your answer is zero, enter 0 Note Dummy origin has supply of 4000 Let x ij amount of units produced by plant node i for customer node j Max fill in the blank 2 x 11 fill in the blank 3 x 12 fill in the blank 4 x 13 fill in the blank 5 x 14 fill in the blank 6 x 21 fill in the blank 7 x 22 fill in the blank 8 x 23 fill in the blank 9 x 24 fill in the blank 10 x 31 fill in the blank 11 x 32 fill in the blank 12 x 33 fill in the blank 13 x 34 s t fill in the blank 14 x 11 fill in the blank 15 x 12 fill in the blank 16 x 13 fill in the blank 17 x 14 fill in the blank 18 fill in the blank 19 x 21 fill in the blank 20 x 22 fill in the blank 21 x 23 fill in the blank 22 x 24 fill in the blank 23 fill in the blank 24 x 31 fill in the blank 25 x 32 fill in the blank 26 x 33 fill in the blank 27 x 34 fill in the blank 28 Dummy fill in the blank 29 x 11 fill in the blank 30 x 21 fill in the blank 31 x 31 fill in the blank 32 fill in the blank 33 x 12 fill in the blank 34 x 22 fill in the blank 35 x 32 fill in the blank 36 fill in the blank 37 x 13 fill in the blank 38 x 23 fill in the blank 39 x 33 fill in the blank 40 fill in the blank 41 x 14 fill in the blank 42 x 24 fill in the blank 43 x 34 fill in the blank 44 x ij 0 for all i , j Units Cost, $ Clifton Springs D 1 fill in the blank 45 fill in the blank 46 Clifton Springs D 2 fill in the blank 47 fill in the blank 48 Clifton Springs D 3 fill in the blank 49 fill in the blank 50 Clifton Springs D 4 fill in the blank 51 fill in the blank 52 Danville D 1 fill in the blank 53 fill in the blank 54 Danville D 2 fill in the blank 55 fill in the blank 56 Danville D 3 fill in the blank 57 fill in the blank 58 Danville D 4 fill in the blank 59 fill in the blank 60 Dummy D 1 fill in the blank 61 fill in the blank 62 Dummy D 2 fill in the blank 63 fill in the blank 64 Dummy D 3 fill in the blank 65 fill in the blank 66 Dummy D 4 fill in the blank 67 fill in the blank 68 Total Cost fill in the blank 69 (Customer 1 2 3 4) demand has a shortfall of (1000 2000 3000 4000 5000) (Customer 1 2 3 4) demand of (1000 2000 3000 4000 5000) is not satisfied

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7. Problem 6-06. PLEASE ANSWER USING THE FORMAT BELOW TO AVOID CONFUSION. OR ELSE, I MIGHT DOWNVOTE. THANK YOU! Klein Chemicals, Inc., produces a special

7. Problem 6-06. PLEASE ANSWER USING THE FORMAT BELOW TO AVOID CONFUSION. OR ELSE, I MIGHT DOWNVOTE. THANK YOU!

Klein Chemicals, Inc., produces a special oil-based material that is currently in short supply. Four of Kleins customers have already placed orders that together exceed the combined capacity of Klein's two plants. Kleins 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 plantcustomer alternative:


	Customer
Plant	D₁	D₂	D₃	D₄
Clifton Springs	$32	$34	$32	$40
Danville	$34	$30	$28	$38

The plant capacities and customer orders are as follows:


Plant	Capacity (units)	Distributor Orders (units)
Clifton Springs	5000	D₁ 2000
		D₂ 5000
Danville	3000	D₃ 3000
		D₄ 2000

How many units should each plant produce for each customer in order to maximize profits? Which customer demands will not be met? Show linear programming formulation. If the constant is "1" it must be entered in the box. If your answer is zero, enter "0".

Note: Dummy origin has supply of 4000.

Let x_ij= amount of units produced by plant node i for customer node j.

Max

fill in the blank 2x₁₁

fill in the blank 3x₁₂

fill in the blank 4x₁₃

fill in the blank 5x₁₄

fill in the blank 6x₂₁

fill in the blank 7x₂₂

fill in the blank 8x₂₃

fill in the blank 9x₂₄

fill in the blank 10x₃₁

fill in the blank 11x₃₂

fill in the blank 12x₃₃

fill in the blank 13x₃₄

s.t.

fill in the blank 14x₁₁

fill in the blank 15x₁₂

fill in the blank 16x₁₃

fill in the blank 17x₁₄

fill in the blank 18

fill in the blank 19x₂₁

fill in the blank 20x₂₂

fill in the blank 21x₂₃

fill in the blank 22x₂₄

fill in the blank 23

fill in the blank 24x₃₁

fill in the blank 25x₃₂

fill in the blank 26x₃₃

fill in the blank 27x₃₄

fill in the blank 28

Dummy

fill in the blank 29x₁₁

fill in the blank 30x₂₁

fill in the blank 31x₃₁

fill in the blank 32

fill in the blank 33x₁₂

fill in the blank 34x₂₂

fill in the blank 35x₃₂

fill in the blank 36

fill in the blank 37x₁₃

fill in the blank 38x₂₃

fill in the blank 39x₃₃

fill in the blank 40

fill in the blank 41x₁₄

fill in the blank 42x₂₄

fill in the blank 43x₃₄

fill in the blank 44

x_ij 0 for all i, j

	Units	Cost, $
Clifton Springs - D₁	fill in the blank 45	fill in the blank 46
Clifton Springs - D₂	fill in the blank 47	fill in the blank 48
Clifton Springs - D₃	fill in the blank 49	fill in the blank 50
Clifton Springs - D₄	fill in the blank 51	fill in the blank 52
Danville - D₁	fill in the blank 53	fill in the blank 54
Danville - D₂	fill in the blank 55	fill in the blank 56
Danville - D₃	fill in the blank 57	fill in the blank 58
Danville - D₄	fill in the blank 59	fill in the blank 60
Dummy - D₁	fill in the blank 61	fill in the blank 62
Dummy - D₂	fill in the blank 63	fill in the blank 64
Dummy - D₃	fill in the blank 65	fill in the blank 66
Dummy - D₄	fill in the blank 67	fill in the blank 68
Total Cost		fill in the blank 69