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 To solve the LP using the extreme point method, we need to graph the feasible region and find the extreme points. 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 Can you kindly explain Graph the constraints and find the extreme points, to get: Feasible region?

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: