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1662637

2030 年全球工業攪拌器市場預測：按類型、安裝類型、組件、結構材料、應用、最終用戶和地區進行分析

Industrial Agitators Market Forecasts to 2030 - Global Analysis By Type, Mounting Type, Component, Material of Construction, Application, End User and By Geography
出版日期: | 出版商: Stratistics Market Research Consulting | 英文 200+ Pages | 商品交期: 2-3個工作天內

價格

根據 Stratistics MRC 的數據，全球工業攪拌機市場規模預計在 2024 年達到 31 億美元，到 2030 年將達到 44 億美元，預測期內的複合年成長率為 6.2%。

工業攪拌機是製造和工業用來混合、攪拌和攪拌容器、儲存槽和反應器中的材料的機械設備。它有助於加速化學反應，改善熱傳遞並保持液體、漿液和粉末的均勻稠度。攪拌器常見於化學、製藥、食品飲料和污水處理等行業，根據應用和所需的混合強度，攪拌器有多種設計，包括槳式、渦輪式和螺旋槳式。

各終端行業的需求不斷增加

工業攪拌機的需求不斷增加，因為它們在化學、製藥、食品和飲料、污水處理等各種終端行業中發揮著至關重要的作用。這些產業需要高效的混合和攪拌解決方案來提高產品品質、縮短加工時間並確保一致性。對自動化的日益關注、生產能力的提高和嚴格的監管要求進一步推動了這些領域對先進、可靠的攪拌系統的需求。

來自低成本製造商的競爭

來自低價製造商的市場競爭可能會帶來一些負面影響，包括現有企業的利潤率降低。為了保持競爭力，公司被迫降低價格，這可能會損害產品品質和客戶服務。此外，低成本競爭對手可能缺乏先進的技術和創新，導致性能不佳和客戶不滿意。這可能會阻礙提供更高品質、更優質解決方案的公司的長期市場成長和品牌知名度。

更加重視流程最佳化

市場重視流程最佳化，其動力來自於提高效率、降低營運成本和改善產品品質的需求。產業專注於最大化產量、最小化能耗以及精確混合以獲得最佳結果。人們正在採用先進的攪拌器設計和自動化技術來改善製程控制、減少停機時間並滿足嚴格的監管標準，從而對創新高效的混合解決方案的需求增加。

初期投資成本高

市場上高昂的初始投資成本可能會阻礙中小企業採用先進的混合技術。這些初始投資成本可能會限制市場滲透，尤其是在成本敏感的行業。此外，公司可能不願意升級現有系統，從而導致營運效率低下和節能解決方案的採用緩慢。這可能會減緩工業成長並阻礙各個行業流程的整體最佳化。

COVID-19 的影響

COVID-19 疫情對市場產生了嚴重影響，導致供應鏈中斷、製造延遲以及汽車和化學品等領域的需求減少。許多行業縮減營運規模，影響銷售。然而，製藥和食品加工等領域的需求增加，以滿足不斷成長的生產需求，包括疫苗製造和基本供應。整體來看，市場面臨挑戰，但也出現成長跡象。

預計在預測期內，機械攪拌器部分將成長至最大的部分。

預計預測期內機械攪拌器將佔據最大的市場佔有率。這些攪拌器利用機械能來引起製程流體的運動，以改善熱傳遞、化學反應和產品一致性。廣泛應用於化工、製藥、食品加工和污水處理等行業。它的效率、客製化選項和耐用性推動了其在各種工業應用領域的需求。

預計預測期內製藥業部門將以最高的複合年成長率成長。

預計預測期內製藥業將呈現最高成長率。攪拌器可確保產品品質一致、增強藥物配方並提高製程效率。攪拌器在懸浮液、乳劑和口服液的生產上不可或缺。隨著監管標準的日益嚴格和對精度的重視，製藥生產對先進、衛生、高效的攪拌機的需求持續成長。

比最大的地區

在預測期內，由於化學、製藥和水處理等行業的需求不斷增加，預計北美將佔據最大的市場佔有率。自動化程度的提高和流程的最佳化正在推動更有效率攪拌機的採用。該地區對技術創新的關注、嚴格的監管標準以及對永續解決方案的需求進一步推動了市場擴張。此外，經濟復甦和產業升級也為市場前景帶來光明。

複合年成長率最高的地區

在預測期內，由於對製造流程的需求不斷增加，預計亞太地區將呈現最高的複合年成長率。化學和製藥業對工業攪拌器的需求源自於製造過程中對精確、高效混合的需求。此外，隨著各行各業努力提高效率和永續性，智慧攪拌器、自動化系統和節能解決方案的採用也推動了市場的發展。

免費客製化服務

訂閱此報告的客戶可享有以下免費自訂選項之一：

  • 公司簡介
    • 對其他市場參與企業（最多 3 家公司）進行全面分析
    • 主要企業的 SWOT 分析（最多 3 家公司）
  • 地理細分
    • 根據客戶興趣對主要國家進行市場估計、預測和複合年成長率（註：基於可行性檢查）
  • 競爭性基準化分析
    • 根據產品系列、地理分佈和策略聯盟對主要企業基準化分析

目錄

第1章執行摘要

第 2 章 前言

  • 概述
  • 相關利益者
  • 研究範圍
  • 調查方法
    • 資料探勘
    • 資料分析
    • 資料檢驗
    • 研究途徑
  • 研究資訊來源
    • 主要研究資訊來源
    • 二手研究資料資訊來源
    • 先決條件

第3章 市場走勢分析

  • 介紹
  • 驅動程式
  • 限制因素
  • 機會
  • 威脅
  • 應用分析
  • 最終用戶分析
  • 新興市場
  • COVID-19 的影響

第 4 章 波特五力分析

  • 供應商的議價能力
  • 買家的議價能力
  • 替代品的威脅
  • 新進入者的威脅
  • 競爭對手之間的競爭

第 5 章 全球工業攪拌機市場按類型

  • 介紹
  • 機械攪拌器
  • 液壓攪拌器
  • 磁力攪拌器
  • 氣動攪拌器
  • 立式攪拌機
  • 臥式攪拌機
  • 其他

6. 全球工業攪拌機市場依安裝類型分類

  • 介紹
  • 頂部安裝
  • 底部安裝
  • 側裝

7. 全球工業攪拌機市場（按組件）

  • 介紹
  • 頭
  • 密封系統
  • 葉輪
  • 其他

8. 全球工業攪拌機市場依結構材料分類

  • 介紹
  • 防鏽的
  • 碳鋼
  • 塑膠
  • 合金

第 9 章 全球工業攪拌機市場（依應用）

  • 介紹
  • 混合物
  • 解散
  • 乳化
  • 暫停
  • 均質化
  • 結晶
  • 其他

第 10 章 全球工業攪拌機市場（依最終用戶分類）

  • 介紹
  • 化工
  • 製藥業
  • 食品飲料業
  • 水處理
  • 石油和天然氣
  • 化妝品和個人護理
  • 礦冶
  • 紙漿和造紙工業
  • 其他

第 11 章 全球工業攪拌機市場（按地區）

  • 介紹
  • 北美洲
    • 美國
    • 加拿大
    • 墨西哥
  • 歐洲
    • 德國
    • 英國
    • 義大利
    • 法國
    • 西班牙
    • 歐洲其他地區
  • 亞太地區
    • 日本
    • 中國
    • 印度
    • 澳洲
    • 紐西蘭
    • 韓國
    • 其他亞太地區
  • 南美洲
    • 阿根廷
    • 巴西
    • 智利
    • 南美洲其他地區
  • 中東和非洲
    • 沙烏地阿拉伯
    • 阿拉伯聯合大公國
    • 卡達
    • 南非
    • 其他中東和非洲地區

第12章 重大進展

  • 協議、夥伴關係、合作和合資企業
  • 收購與合併
  • 新產品發布
  • 業務擴展
  • 其他關鍵策略

第13章 公司概況

  • SPX Flow
  • Alfa Laval
  • Flender
  • Chemineer
  • Admix
  • Schenck Process
  • KSB Group
  • CEM International
  • Xylem Inc.
  • Rotorflush
  • GEA Group
  • Eaton
  • Mitsubishi Heavy Industries
  • Globalmix
  • TecnoMix
  • Rexnord
Product Code: SMRC28498

According to Stratistics MRC, the Global Industrial Agitators Market is accounted for $3.1 billion in 2024 and is expected to reach $4.4 billion by 2030 growing at a CAGR of 6.2% during the forecast period. Industrial agitators are mechanical devices used in manufacturing and processing industries to mix, blend, or stir substances within a vessel, tank, or reactor. They help enhance chemical reactions, improve heat transfer, and maintain uniform consistency in liquids, slurries, or powders. Commonly found in industries such as chemicals, pharmaceuticals, food and beverages, and wastewater treatment, agitators come in various designs, including paddle, turbine, and propeller types, depending on the application and required mixing intensity.

Market Dynamics:

Driver:

Rising demand from various end-use industries

The rising demand for industrial agitators is driven by their crucial role in various end-use industries, including chemicals, pharmaceuticals, food and beverages, and wastewater treatment. These industries require efficient mixing and blending solutions to enhance product quality, improve processing times, and ensure consistency. The growing emphasis on automation, increasing production capacities, and stringent regulatory requirements further boost the demand for advanced and reliable agitator systems in these sectors.

Restraint:

Competition from low-cost manufacturers

Competition from low-cost manufacturers in the market can lead to several negative effects, such as reduced profit margins for established companies. To stay competitive, firms may be forced to lower prices, potentially compromising product quality or customer service. Additionally, low-cost competitors may lack advanced technology or innovation, leading to suboptimal performance and customer dissatisfaction. This can hinder long-term market growth and brand reputation for companies offering higher-quality, premium solutions.

Opportunity:

Growing emphasis on process optimization

The growing emphasis on process optimization in the market is driven by the need for increased efficiency, reduced operational costs, and enhanced product quality. Industries are focusing on maximizing throughput, minimizing energy consumption, and ensuring precise mixing to achieve optimal results. Advanced agitator designs and automation technologies are being adopted to improve process control, reduce downtime, and meet stringent regulatory standards, leading to higher demand for innovative and efficient agitation solutions.

Threat:

High initial investment costs

High initial investment costs in the market can deter small and medium-sized enterprises (SMEs) from adopting advanced mixing technologies. These upfront costs may limit market penetration, especially in cost-sensitive industries. Additionally, companies may hesitate to upgrade their existing systems, leading to inefficient operations or delayed adoption of more energy-efficient solutions. This can slow down industry growth and hinder the overall optimization of processes in various sectors.

Covid-19 Impact:

The COVID-19 pandemic significantly impacted the market, causing disruptions in supply chains, manufacturing delays, and a decline in demand from sectors like automotive and chemicals. Many industries scaled back operations, affecting sales. However, sectors like pharmaceuticals and food processing saw increased demand as they adapted to heightened production needs, such as vaccine manufacturing and essential goods. Overall, the market faced challenges but also experienced some areas of growth.

The mechanical agitators segment is expected to be the largest during the forecast period

The mechanical agitators segment is expected to account for the largest market share during the forecast period. These agitators employ mechanical energy to induce motion in the process fluid, improving heat transfer, chemical reactions, and product consistency. They are widely used in industries such as chemicals, pharmaceuticals, food processing, and wastewater treatment. Their efficiency, customization options, and durability drive demand in various industrial applications.

The pharmaceutical industry segment is expected to have the highest CAGR during the forecast period

Over the forecast period, the pharmaceutical industry segment is predicted to witness the highest growth rate. They ensure consistent product quality, enhance drug formulation, and improve process efficiency. Agitators are vital in producing suspensions, emulsions, and oral liquid formulations. With strict regulatory standards and a focus on precision, demand for advanced, sanitary, and efficient agitators in pharmaceutical manufacturing continues to grow.

Region with largest share:

During the forecast period, the North America region is expected to hold the largest market share due to increased demand from industries like chemicals, pharmaceuticals, and water treatment. Advancements in automation and process optimization are driving the adoption of more efficient agitators. The region's focus on innovation, strict regulatory standards, and the need for sustainable solutions further boost market expansion. Additionally, a recovering economy and industrial upgrades contribute to the market's positive outlook.

Region with highest CAGR:

Over the forecast period, the Asia Pacific region is anticipated to exhibit the highest CAGR due to increasing demand for manufacturing processes. The demand for industrial agitators in the chemical and pharmaceutical industries is rising due to the need for precise and high-efficiency mixing in production processes. Additionally, the adoption of smart agitators, automated systems, and energy-efficient solutions is also boosting the market, as industries strive for increased efficiency and sustainability.

Key players in the market

Some of the key players in Industrial Agitators market include SPX Flow, Alfa Laval, Flender, Chemineer, Admix, Schenck Process, KSB Group, CEM International, Xylem Inc., Rotorflush, GEA Group, Eaton, Mitsubishi Heavy Industries, Globalmix, TecnoMix and Rexnord.

Key Developments:

In January 2025, Eaton announced that its portfolio of switches, circuit protection and power distribution products for commercial vehicles is now available to aftermarket customers. It said the move addresses the growing demand for electrical power management solutions that support the evolving needs of the aftermarket industry.

In May 2024, Xylem announced the launch of Reuse Brew, a Bavarian beer to address the rising water scarcity. This beer, crafted from top-quality treated wastewater, represents a major leap forward in water recycling technology, providing a sustainable solution to the rising challenges posed by climate change.

Types Covered:

  • Mechanical Agitators
  • Hydraulic Agitators
  • Magnetic Agitators
  • Air-Driven Agitators
  • Vertical Agitators
  • Horizontal Agitators
  • Other Types

Mounting Types Covered:

  • Top-Mounted
  • Bottom-Mounted
  • Side-Mounted

Components Covered:

  • Heads
  • Sealing Systems
  • Impellers
  • Other Components

Material of Constructions Covered:

  • Stainless Steel
  • Carbon Steel
  • Plastic
  • Alloys

Applications Covered:

  • Mixing
  • Dissolving
  • Emulsification
  • Suspension
  • Homogenization
  • Crystallization
  • Other Applications

End Users Covered:

  • Chemical Industry
  • Pharmaceutical Industry
  • Food and Beverage Industry
  • Water Treatment
  • Oil & Gas Industry
  • Cosmetic and Personal Care
  • Mining and Metallurgy
  • Pulp and Paper Industry
  • Other End Users

Regions Covered:

  • North America
    • US
    • Canada
    • Mexico
  • Europe
    • Germany
    • UK
    • Italy
    • France
    • Spain
    • Rest of Europe
  • Asia Pacific
    • Japan
    • China
    • India
    • Australia
    • New Zealand
    • South Korea
    • Rest of Asia Pacific
  • South America
    • Argentina
    • Brazil
    • Chile
    • Rest of South America
  • Middle East & Africa
    • Saudi Arabia
    • UAE
    • Qatar
    • South Africa
    • Rest of Middle East & Africa

What our report offers:

  • Market share assessments for the regional and country-level segments
  • Strategic recommendations for the new entrants
  • Covers Market data for the years 2022, 2023, 2024, 2026, and 2030
  • Market Trends (Drivers, Constraints, Opportunities, Threats, Challenges, Investment Opportunities, and recommendations)
  • Strategic recommendations in key business segments based on the market estimations
  • Competitive landscaping mapping the key common trends
  • Company profiling with detailed strategies, financials, and recent developments
  • Supply chain trends mapping the latest technological advancements

Free Customization Offerings:

All the customers of this report will be entitled to receive one of the following free customization options:

  • Company Profiling
    • Comprehensive profiling of additional market players (up to 3)
    • SWOT Analysis of key players (up to 3)
  • Regional Segmentation
    • Market estimations, Forecasts and CAGR of any prominent country as per the client's interest (Note: Depends on feasibility check)
  • Competitive Benchmarking
    • Benchmarking of key players based on product portfolio, geographical presence, and strategic alliances

Table of Contents

1 Executive Summary

2 Preface

  • 2.1 Abstract
  • 2.2 Stake Holders
  • 2.3 Research Scope
  • 2.4 Research Methodology
    • 2.4.1 Data Mining
    • 2.4.2 Data Analysis
    • 2.4.3 Data Validation
    • 2.4.4 Research Approach
  • 2.5 Research Sources
    • 2.5.1 Primary Research Sources
    • 2.5.2 Secondary Research Sources
    • 2.5.3 Assumptions

3 Market Trend Analysis

  • 3.1 Introduction
  • 3.2 Drivers
  • 3.3 Restraints
  • 3.4 Opportunities
  • 3.5 Threats
  • 3.6 Application Analysis
  • 3.7 End User Analysis
  • 3.8 Emerging Markets
  • 3.9 Impact of Covid-19

4 Porters Five Force Analysis

  • 4.1 Bargaining power of suppliers
  • 4.2 Bargaining power of buyers
  • 4.3 Threat of substitutes
  • 4.4 Threat of new entrants
  • 4.5 Competitive rivalry

5 Global Industrial Agitators Market, By Type

  • 5.1 Introduction
  • 5.2 Mechanical Agitators
  • 5.3 Hydraulic Agitators
  • 5.4 Magnetic Agitators
  • 5.5 Air-Driven Agitators
  • 5.6 Vertical Agitators
  • 5.7 Horizontal Agitators
  • 5.8 Other Types

6 Global Industrial Agitators Market, By Mounting Type

  • 6.1 Introduction
  • 6.2 Top-Mounted
  • 6.3 Bottom-Mounted
  • 6.4 Side-Mounted

7 Global Industrial Agitators Market, By Component

  • 7.1 Introduction
  • 7.2 Heads
  • 7.3 Sealing Systems
  • 7.4 Impellers
  • 7.5 Other Components

8 Global Industrial Agitators Market, By Material of Construction

  • 8.1 Introduction
  • 8.2 Stainless Steel
  • 8.3 Carbon Steel
  • 8.4 Plastic
  • 8.5 Alloys

9 Global Industrial Agitators Market, By Application

  • 9.1 Introduction
  • 9.2 Mixing
  • 9.3 Dissolving
  • 9.4 Emulsification
  • 9.5 Suspension
  • 9.6 Homogenization
  • 9.7 Crystallization
  • 9.8 Other Applications

10 Global Industrial Agitators Market, By End User

  • 10.1 Introduction
  • 10.2 Chemical Industry
  • 10.3 Pharmaceutical Industry
  • 10.4 Food and Beverage Industry
  • 10.5 Water Treatment
  • 10.6 Oil & Gas Industry
  • 10.7 Cosmetic and Personal Care
  • 10.8 Mining and Metallurgy
  • 10.9 Pulp and Paper Industry
  • 10.10 Other End Users

11 Global Industrial Agitators Market, By Geography

  • 11.1 Introduction
  • 11.2 North America
    • 11.2.1 US
    • 11.2.2 Canada
    • 11.2.3 Mexico
  • 11.3 Europe
    • 11.3.1 Germany
    • 11.3.2 UK
    • 11.3.3 Italy
    • 11.3.4 France
    • 11.3.5 Spain
    • 11.3.6 Rest of Europe
  • 11.4 Asia Pacific
    • 11.4.1 Japan
    • 11.4.2 China
    • 11.4.3 India
    • 11.4.4 Australia
    • 11.4.5 New Zealand
    • 11.4.6 South Korea
    • 11.4.7 Rest of Asia Pacific
  • 11.5 South America
    • 11.5.1 Argentina
    • 11.5.2 Brazil
    • 11.5.3 Chile
    • 11.5.4 Rest of South America
  • 11.6 Middle East & Africa
    • 11.6.1 Saudi Arabia
    • 11.6.2 UAE
    • 11.6.3 Qatar
    • 11.6.4 South Africa
    • 11.6.5 Rest of Middle East & Africa

12 Key Developments

  • 12.1 Agreements, Partnerships, Collaborations and Joint Ventures
  • 12.2 Acquisitions & Mergers
  • 12.3 New Product Launch
  • 12.4 Expansions
  • 12.5 Other Key Strategies

13 Company Profiling

  • 13.1 SPX Flow
  • 13.2 Alfa Laval
  • 13.3 Flender
  • 13.4 Chemineer
  • 13.5 Admix
  • 13.6 Schenck Process
  • 13.7 KSB Group
  • 13.8 CEM International
  • 13.9 Xylem Inc.
  • 13.10 Rotorflush
  • 13.11 GEA Group
  • 13.12 Eaton
  • 13.13 Mitsubishi Heavy Industries
  • 13.14 Globalmix
  • 13.15 TecnoMix
  • 13.16 Rexnord

List of Tables

  • Table 1 Global Industrial Agitators Market Outlook, By Region (2022-2030) ($MN)
  • Table 2 Global Industrial Agitators Market Outlook, By Type (2022-2030) ($MN)
  • Table 3 Global Industrial Agitators Market Outlook, By Mechanical Agitators (2022-2030) ($MN)
  • Table 4 Global Industrial Agitators Market Outlook, By Hydraulic Agitators (2022-2030) ($MN)
  • Table 5 Global Industrial Agitators Market Outlook, By Magnetic Agitators (2022-2030) ($MN)
  • Table 6 Global Industrial Agitators Market Outlook, By Air-Driven Agitators (2022-2030) ($MN)
  • Table 7 Global Industrial Agitators Market Outlook, By Vertical Agitators (2022-2030) ($MN)
  • Table 8 Global Industrial Agitators Market Outlook, By Horizontal Agitators (2022-2030) ($MN)
  • Table 9 Global Industrial Agitators Market Outlook, By Other Types (2022-2030) ($MN)
  • Table 10 Global Industrial Agitators Market Outlook, By Mounting Type (2022-2030) ($MN)
  • Table 11 Global Industrial Agitators Market Outlook, By Top-Mounted (2022-2030) ($MN)
  • Table 12 Global Industrial Agitators Market Outlook, By Bottom-Mounted (2022-2030) ($MN)
  • Table 13 Global Industrial Agitators Market Outlook, By Side-Mounted (2022-2030) ($MN)
  • Table 14 Global Industrial Agitators Market Outlook, By Component (2022-2030) ($MN)
  • Table 15 Global Industrial Agitators Market Outlook, By Heads (2022-2030) ($MN)
  • Table 16 Global Industrial Agitators Market Outlook, By Sealing Systems (2022-2030) ($MN)
  • Table 17 Global Industrial Agitators Market Outlook, By Impellers (2022-2030) ($MN)
  • Table 18 Global Industrial Agitators Market Outlook, By Other Components (2022-2030) ($MN)
  • Table 19 Global Industrial Agitators Market Outlook, By Material of Construction (2022-2030) ($MN)
  • Table 20 Global Industrial Agitators Market Outlook, By Stainless Steel (2022-2030) ($MN)
  • Table 21 Global Industrial Agitators Market Outlook, By Carbon Steel (2022-2030) ($MN)
  • Table 22 Global Industrial Agitators Market Outlook, By Plastic (2022-2030) ($MN)
  • Table 23 Global Industrial Agitators Market Outlook, By Alloys (2022-2030) ($MN)
  • Table 24 Global Industrial Agitators Market Outlook, By Application (2022-2030) ($MN)
  • Table 25 Global Industrial Agitators Market Outlook, By Mixing (2022-2030) ($MN)
  • Table 26 Global Industrial Agitators Market Outlook, By Dissolving (2022-2030) ($MN)
  • Table 27 Global Industrial Agitators Market Outlook, By Emulsification (2022-2030) ($MN)
  • Table 28 Global Industrial Agitators Market Outlook, By Suspension (2022-2030) ($MN)
  • Table 29 Global Industrial Agitators Market Outlook, By Homogenization (2022-2030) ($MN)
  • Table 30 Global Industrial Agitators Market Outlook, By Crystallization (2022-2030) ($MN)
  • Table 31 Global Industrial Agitators Market Outlook, By Other Applications (2022-2030) ($MN)
  • Table 32 Global Industrial Agitators Market Outlook, By End User (2022-2030) ($MN)
  • Table 33 Global Industrial Agitators Market Outlook, By Chemical Industry (2022-2030) ($MN)
  • Table 34 Global Industrial Agitators Market Outlook, By Pharmaceutical Industry (2022-2030) ($MN)
  • Table 35 Global Industrial Agitators Market Outlook, By Food and Beverage Industry (2022-2030) ($MN)
  • Table 36 Global Industrial Agitators Market Outlook, By Water Treatment (2022-2030) ($MN)
  • Table 37 Global Industrial Agitators Market Outlook, By Oil & Gas Industry (2022-2030) ($MN)
  • Table 38 Global Industrial Agitators Market Outlook, By Cosmetic and Personal Care (2022-2030) ($MN)
  • Table 39 Global Industrial Agitators Market Outlook, By Mining and Metallurgy (2022-2030) ($MN)
  • Table 40 Global Industrial Agitators Market Outlook, By Pulp and Paper Industry (2022-2030) ($MN)
  • Table 41 Global Industrial Agitators Market Outlook, By Other End Users (2022-2030) ($MN)

Note: Tables for North America, Europe, APAC, South America, and Middle East & Africa Regions are also represented in the same manner as above.