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
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