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 (W1) 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: Write the objective function and the constraint in equations. Let V¡¡tons shipped to customer i from warehouse j, and so on. For example, = tons shipped to customer A from warehouse W1. VA1 This exercise contains only parts b, c, d, e, and f. b) The objective function for the LP model = Minimize Z = c) Subject to: $7.50 $6.75 +$6.25 + $7.00 Customer A Customer B For all Vij 20 ▼+$6.50 + $8.00 + W 1 $7.50 $6.75 W 2 $6.25 $7.00 Customer A's demand Customer B's demand Warehouse 1's supply Warehouse 2's supply Warehouse 3's supply non negativity condition W 3 $6.50 $8.00 (shipping cost to customer A) (shipping cost to customer B)
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 (W1) 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: Write the objective function and the constraint in equations. Let V¡¡tons shipped to customer i from warehouse j, and so on. For example, = tons shipped to customer A from warehouse W1. VA1 This exercise contains only parts b, c, d, e, and f. b) The objective function for the LP model = Minimize Z = c) Subject to: $7.50 $6.75 +$6.25 + $7.00 Customer A Customer B For all Vij 20 ▼+$6.50 + $8.00 + W 1 $7.50 $6.75 W 2 $6.25 $7.00 Customer A's demand Customer B's demand Warehouse 1's supply Warehouse 2's supply Warehouse 3's supply non negativity condition W 3 $6.50 $8.00 (shipping cost to customer A) (shipping cost to customer B)
Purchasing and Supply Chain Management
6th Edition
ISBN:9781285869681
Author:Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. Patterson
Publisher:Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. Patterson
ChapterC: Cases
Section: Chapter Questions
Problem 5.1SC: Scenario 3 Ben Gibson, the purchasing manager at Coastal Products, was reviewing purchasing...
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B & C
![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 (W1) 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:
This exercise contains only parts b, c, d, e, and f.
b) The objective function for the LP model =
Minimize Z =
c) Subject to:
$7.50
$6.75
Customer A
Customer B
Write the objective function and the constraint in equations. Let V₁;= tons shipped to customer i from warehouse j, and so on. For example,
VA1 = tons shipped to customer A from warehouse W1.
+ $6.25
+ $7.00
For all Vij 20
+ $6.50
+ $8.00
W 1
$7.50
$6.75
+
W 2
$6.25
$7.00
W 3
Customer A's demand
Customer B's demand
Warehouse 1's supply
Warehouse 2's supply
Warehouse 3's supply
non negativity condition
$6.50
$8.00
(shipping cost to customer A)
(shipping cost to customer B)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0a63f6a7-ec54-4c0e-abf5-810ded572838%2Ff1d3826b-0d9b-4aca-a2a2-0bd99dcb10ab%2F76nzus4_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 (W1) 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:
This exercise contains only parts b, c, d, e, and f.
b) The objective function for the LP model =
Minimize Z =
c) Subject to:
$7.50
$6.75
Customer A
Customer B
Write the objective function and the constraint in equations. Let V₁;= tons shipped to customer i from warehouse j, and so on. For example,
VA1 = tons shipped to customer A from warehouse W1.
+ $6.25
+ $7.00
For all Vij 20
+ $6.50
+ $8.00
W 1
$7.50
$6.75
+
W 2
$6.25
$7.00
W 3
Customer A's demand
Customer B's demand
Warehouse 1's supply
Warehouse 2's supply
Warehouse 3's supply
non negativity condition
$6.50
$8.00
(shipping cost to customer A)
(shipping cost to customer B)
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