A company has two alkylate plants, A1 and A2, from which a given product is distributed to customers C1, C2, and C3. The transportation costs are given as follows: Plants Customer A1 A1 A1 A₂ A2 A₂ C1 C2 C3 C1 C2 C3 Cost ($/ton) 25 60 75 20 50 85 The maximum refinery production rates and minimum customer demand rates are as follows: Customer/plant Rate, tons/day A1 A₂ C1 C2 C3 1.6 0.8 0.9 0.7 0.3 The cost of production for A₁ is $30/ton for production levels less than 0.5 ton/day; for production greater than 0.5 ton/day, the production cost is $40/ton. The production cost of A2 is uniform at $35/ton. Find the optimum distribution policy to minimize the company's total costs.

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A company has two alkylate plants, A1 and A2, from which a given product is distributed
to customers C1, C2, and C3. The transportation costs are given as follows:
Plants
Customer
A1
A1
A1
A₂
A2
A₂
C1
C2
C3
C1
C2
C3
Cost ($/ton)
25
60
75
20
50
85
The maximum refinery production rates and minimum customer demand rates are as follows:
Customer/plant
Rate, tons/day
A1
A₂
C1
C2
C3
1.6
0.8
0.9
0.7
0.3
The cost of production for A₁ is $30/ton for production levels less than 0.5 ton/day; for production
greater than 0.5 ton/day, the production cost is $40/ton. The production cost of A2 is uniform at
$35/ton. Find the optimum distribution policy to minimize the company's total costs.
Transcribed Image Text:A company has two alkylate plants, A1 and A2, from which a given product is distributed to customers C1, C2, and C3. The transportation costs are given as follows: Plants Customer A1 A1 A1 A₂ A2 A₂ C1 C2 C3 C1 C2 C3 Cost ($/ton) 25 60 75 20 50 85 The maximum refinery production rates and minimum customer demand rates are as follows: Customer/plant Rate, tons/day A1 A₂ C1 C2 C3 1.6 0.8 0.9 0.7 0.3 The cost of production for A₁ is $30/ton for production levels less than 0.5 ton/day; for production greater than 0.5 ton/day, the production cost is $40/ton. The production cost of A2 is uniform at $35/ton. Find the optimum distribution policy to minimize the company's total costs.
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