A firm has two stores and two warehouses. The transportation costs from warehouse 1 is $18 to store 1 and $9 to store 2. The transportation costs from warehouse 2 is $24 to store 1 and $15 to store 2. Warehouse 1 has a capacity of 45 and warehouse 2 has a capacity of 40. Each store makes their order at the beginning of the period. Store 1 orders 25 units and store 2 orders 30 units. The firm is trying to minimize their transportation costs. Let: x1 = units transported from warehouse 1 to store 1 x2 = units transported from warehouse 1 to store 2 x3 = units transported from warehouse 2 to store 1 x4 = units transported from warehouse 2 to store 2 The objective function is to minimize the transportation costs: Minimize: 18x1 + 9x2 + 24x3 + 15x4 Subject to: Warehouse 1 capacity constraint: x1 + x2 ≤ 45 Warehouse 2 capacity constraint: x3 + x4 ≤ 40 Store 1 demand constraint: x1 + x3 = 25 Store 2 demand constraint: x2 + x4 = 30 Non-negativity constraint: x1, x2, x3, x4 ≥ 0 How to Graph the constraints to find the extreme points, Feasible region? Can you kindly explain.
A firm has two stores and two warehouses. The transportation costs from warehouse 1 is $18 to store 1 and $9 to store 2. The transportation costs from warehouse 2 is $24 to store 1 and $15 to store 2. Warehouse 1 has a capacity of 45 and warehouse 2 has a capacity of 40. Each store makes their order at the beginning of the period. Store 1 orders 25 units and store 2 orders 30 units. The firm is trying to minimize their transportation costs. Let: x1 = units transported from warehouse 1 to store 1 x2 = units transported from warehouse 1 to store 2 x3 = units transported from warehouse 2 to store 1 x4 = units transported from warehouse 2 to store 2 The objective function is to minimize the transportation costs: Minimize: 18x1 + 9x2 + 24x3 + 15x4 Subject to: Warehouse 1 capacity constraint: x1 + x2 ≤ 45 Warehouse 2 capacity constraint: x3 + x4 ≤ 40 Store 1 demand constraint: x1 + x3 = 25 Store 2 demand constraint: x2 + x4 = 30 Non-negativity constraint: x1, x2, x3, x4 ≥ 0 How to Graph the constraints to find the extreme points, Feasible region? Can you kindly explain.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A firm has two stores and two warehouses. The transportation costs from warehouse 1 is $18 to store 1 and $9 to store 2. The transportation costs from warehouse 2 is $24 to store 1 and $15 to store 2. Warehouse 1 has a capacity of 45 and warehouse 2 has a capacity of 40. Each store makes their order at the beginning of the period. Store 1 orders 25 units and store 2 orders 30 units. The firm is trying to minimize their transportation costs.
Let:
- x1 = units transported from warehouse 1 to store 1
- x2 = units transported from warehouse 1 to store 2
- x3 = units transported from warehouse 2 to store 1
- x4 = units transported from warehouse 2 to store 2
The objective function is to minimize the transportation costs:
Minimize: 18x1 + 9x2 + 24x3 + 15x4
Subject to:
- Warehouse 1 capacity constraint: x1 + x2 ≤ 45
- Warehouse 2 capacity constraint: x3 + x4 ≤ 40
- Store 1 demand constraint: x1 + x3 = 25
- Store 2 demand constraint: x2 + x4 = 30
- Non-negativity constraint: x1, x2, x3, x4 ≥ 0
How to Graph the constraints to find the extreme points, Feasible region? Can you kindly explain.
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