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You manage a chemical company with 2 warehouses. The following quantities of Important Chemical A have arrived from an international supplier at 3 different ports: Chemical Available (L) Port 1 400 Port 2 110 Port 3 100 The following amounts of Important Chemical A are required at your warehouses: Warehouse 1 Warehouse 2 Chemical Required (L) 380 230 The cost in£to ship 1L of chemical from each port to each warehouse is as follows: Warehouse 1 Warehouse 2 Port 1 £10 Port 2 £20 Port 3 £13 £45 £28 £11 (a) You want to know how to send these shipments as cheaply as possible. For- mulate this as a linear program (you do not need to formulate it in standard inequality form) indicating what each variable represents. (b) Suppose now that all is as in the previous question but that only 320L of Important Chemical A are now required at Warehouse 1. Any excess chemical can be transported to either Warehouse 1 or 2 for storage, in which case the company must pay only the relevant transportation costs, or can be disposed of at the port in which case the company pays no transportation costs but pays a disposal fee of £16 per L. You want to find out how to ship or dispose of all 610L of chemical imported at a minimum cost, while still ensuring that the required amounts (320L and 230L, respectively) are delivered to Warehouse 1 and 2. Describe how to modify your linear program from the previous question to model this problem.

You manage a chemical company with 2 warehouses. The following quantities of Important Chemical A have arrived from an international supplier at 3 different ports: Chemical Available (L) Port 1 400 Port 2 110 Port 3 100 The following amounts of Important Chemical A are required at your warehouses: Warehouse 1 Warehouse 2 Chemical Required (L) 380 230 The cost in£to ship 1L of chemical from each port to each warehouse is as follows: Warehouse 1 Warehouse 2 Port 1 £10 Port 2 £20 Port 3 £13 £45 £28 £11 (a) You want to know how to send these shipments as cheaply as possible. For- mulate this as a linear program (you do not need to formulate it in standard inequality form) indicating what each variable represents. (b) Suppose now that all is as in the previous question but that only 320L of Important Chemical A are now required at Warehouse 1. Any excess chemical can be transported to either Warehouse 1 or 2 for storage, in which case the company must pay only the relevant transportation costs, or can be disposed of at the port in which case the company pays no transportation costs but pays a disposal fee of £16 per L. You want to find out how to ship or dispose of all 610L of chemical imported at a minimum cost, while still ensuring that the required amounts (320L and 230L, respectively) are delivered to Warehouse 1 and 2. Describe how to modify your linear program from the previous question to model this problem.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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You manage a chemical company with 2 warehouses. The following quantities of Important Chemical A have arrived from an international supplier at 3 different ports: Chemical Available (L) Port 1 400 Port 2 110 Port 3 100 The following amounts of Important Chemical A are required at your warehouses: Warehouse 1 Warehouse 2 Chemical Required (L) 380 230 The cost in£to ship 1L of chemical from each port to each warehouse is as follows: Warehouse 1 Warehouse 2 Port 1 £10 Port 2 £20 Port 3 £13 £45 £28 £11 (a) You want to know how to send these shipments as cheaply as possible. For- mulate this as a linear program (you do not need to formulate it in standard inequality form) indicating what each variable represents. (b) Suppose now that all is as in the previous question but that only 320L of Important Chemical A are now required at Warehouse 1. Any excess chemical can be transported to either Warehouse 1 or 2 for storage, in which case the company must pay only the relevant transportation costs, or can be disposed of at the port in which case the company pays no transportation costs but pays a disposal fee of £16 per L. You want to find out how to ship or dispose of all 610L of chemical imported at a minimum cost, while still ensuring that the required amounts (320L and 230L, respectively) are delivered to Warehouse 1 and 2. Describe how to modify your linear program from the previous question to model this problem.
Transcribed Image Text:You manage a chemical company with 2 warehouses. The following quantities of Important Chemical A have arrived from an international supplier at 3 different ports: Chemical Available (L) Port 1 400 Port 2 110 Port 3 100 The following amounts of Important Chemical A are required at your warehouses: Warehouse 1 Warehouse 2 Chemical Required (L) 380 230 The cost in£to ship 1L of chemical from each port to each warehouse is as follows: Warehouse 1 Warehouse 2 Port 1 £10 Port 2 £20 Port 3 £13 £45 £28 £11 (a) You want to know how to send these shipments as cheaply as possible. For- mulate this as a linear program (you do not need to formulate it in standard inequality form) indicating what each variable represents. (b) Suppose now that all is as in the previous question but that only 320L of Important Chemical A are now required at Warehouse 1. Any excess chemical can be transported to either Warehouse 1 or 2 for storage, in which case the company must pay only the relevant transportation costs, or can be disposed of at the port in which case the company pays no transportation costs but pays a disposal fee of £16 per L. You want to find out how to ship or dispose of all 610L of chemical imported at a minimum cost, while still ensuring that the required amounts (320L and 230L, respectively) are delivered to Warehouse 1 and 2. Describe how to modify your linear program from the previous question to model this problem.
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