A fertilizer manufacturer has to fulfill supply contracts to its two main customers (650 tons to Customer A and 800 tons to Customer B). It can meet this demand by shipping existing inventory from any of its three warehouses. Warehouse has 400 tons of inventory onhand, Warehouse 2 (Ww2) has 500 tons, and Warehouse 3 (W3) has 600 tons. The company would like to arrange the shipping for the lowest cost possible, where the per-ton transit costs are as follows: W1 W 2 W 3 Customer A $7.50 $6.25 $6.50 Customer B $6.75 $7.00 $8.00 Write the objective function and the constraint in equations. Let V= tons shipped to customer i from warehouse j, and so on. For example, Va1 = tons shipped to customer A from warehouse W1. This exercise contains only parts b, c, d, e, and f. b) The objective function for the LP model = Minimize Z= $7.50 V+ $6.25 V+ $6.50 (shipping cost to customer A) $6.75 v +$7.00 V + $8.00 (shipping cost to customer B) c) Subject to: Customer A's demand Customer B's demand Warehouse 1's supply Warehouse 2's supply Warehouse 3's supply For all Vy 20 non negativity condition
A fertilizer manufacturer has to fulfill supply contracts to its two main customers (650 tons to Customer A and 800 tons to Customer B). It can meet this demand by shipping existing inventory from any of its three warehouses. Warehouse has 400 tons of inventory onhand, Warehouse 2 (Ww2) has 500 tons, and Warehouse 3 (W3) has 600 tons. The company would like to arrange the shipping for the lowest cost possible, where the per-ton transit costs are as follows: W1 W 2 W 3 Customer A $7.50 $6.25 $6.50 Customer B $6.75 $7.00 $8.00 Write the objective function and the constraint in equations. Let V= tons shipped to customer i from warehouse j, and so on. For example, Va1 = tons shipped to customer A from warehouse W1. This exercise contains only parts b, c, d, e, and f. b) The objective function for the LP model = Minimize Z= $7.50 V+ $6.25 V+ $6.50 (shipping cost to customer A) $6.75 v +$7.00 V + $8.00 (shipping cost to customer B) c) Subject to: Customer A's demand Customer B's demand Warehouse 1's supply Warehouse 2's supply Warehouse 3's supply For all Vy 20 non negativity condition
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter5: Network Models
Section: Chapter Questions
Problem 68P
Related questions
Question
![A fertilizer manufacturer has to fulfill supply contracts to its two main customers (650 tons to Customer A and 800 tons to Customer B). It can meet this demand by shipping existing inventory from any of its three warehouses. Warehouse 1
has 400 tons of inventory onhand, Warehouse 2 (W2) has 500 tons, and Warehouse 3 (W3) has 600 tons. The company would like to arrange the shipping for the lowest cost possible, where the per-ton transit costs are as follows:
W 1
W 2
W 3
$7.50
$6.75
$6.25
$7.00
$6.50
$8.00
Customer A
Customer B
Write the objective function and the constraint in equations. Let V;= tons shipped to customer i from warehouse j, and so on. For example, VA1 = tons shipped to customer A from warehouse W1.
This exercise contains only parts b, c, d, e, and f.
b) The objective function for the LP model =
Minimize Z =
$7.50
+ $6.25
+ $6.50
(shipping cost to customer A)
V +
$6.75
+ $7.00
+ $8.00
(shipping cost to customer B)
c) Subject to:
Customer A's demand
Customer B's demand
Warehouse 1's supply
Warehouse 2's supply
Warehouse 3's supply
For all Vj 20
non negativity condition](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96bc6193-a9e7-4716-b78f-2b2e254dbd91%2F7477782d-3598-43cd-a746-5a198d4480ac%2Foaw5y3_processed.png&w=3840&q=75)
Transcribed Image Text:A fertilizer manufacturer has to fulfill supply contracts to its two main customers (650 tons to Customer A and 800 tons to Customer B). It can meet this demand by shipping existing inventory from any of its three warehouses. Warehouse 1
has 400 tons of inventory onhand, Warehouse 2 (W2) has 500 tons, and Warehouse 3 (W3) has 600 tons. The company would like to arrange the shipping for the lowest cost possible, where the per-ton transit costs are as follows:
W 1
W 2
W 3
$7.50
$6.75
$6.25
$7.00
$6.50
$8.00
Customer A
Customer B
Write the objective function and the constraint in equations. Let V;= tons shipped to customer i from warehouse j, and so on. For example, VA1 = tons shipped to customer A from warehouse W1.
This exercise contains only parts b, c, d, e, and f.
b) The objective function for the LP model =
Minimize Z =
$7.50
+ $6.25
+ $6.50
(shipping cost to customer A)
V +
$6.75
+ $7.00
+ $8.00
(shipping cost to customer B)
c) Subject to:
Customer A's demand
Customer B's demand
Warehouse 1's supply
Warehouse 2's supply
Warehouse 3's supply
For all Vj 20
non negativity condition
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Practical Management Science](https://www.bartleby.com/isbn_cover_images/9781337406659/9781337406659_smallCoverImage.gif)
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
![Practical Management Science](https://www.bartleby.com/isbn_cover_images/9781337406659/9781337406659_smallCoverImage.gif)
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,