Multi-Product Quantity-Dependent Prices and Profitability Constraints

The Experience
- Overview of The Experience
- About Us
  - Overview of Stanford GSB
  - The Leadership
    - Overview of The Leadership
    - Updates
    - Advisory Council
      - Overview of Advisory Council
      - Members
  - Centers & Institutes
    - Overview of Centers & Institutes
    - Center for Entrepreneurial Studies
      - Overview of Center for Entrepreneurial Studies
      - Research
        
        Overview of Research
        
        Search Funds
        
        Overview of Search Funds
        
        Search Fund Primer
      - Teaching & Curriculum
      - Faculty & Staff
        
        Overview of Faculty & Staff
        
        Affiliated Faculty
        
        Faculty Advisors
      - Contact
        
        View Contact Information
        
        Louis W. Foster Resource Center
    - Center for Social Innovation
      - Overview of Center for Social Innovation
      - Defining Social Innovation
      - Impact Compass
      - Global Health Innovation Insights
      - Faculty & Staff
        
        Faculty Affiliates
      - Contact
  - School Profile
  - Our Alumni
- School News & History
  - Overview of School News & History
  - Our History
  - Commencement
    - Overview of Commencement
    - Class of 2020
    - Class of 2022
    - Certificate & Award Recipients
      - Overview of Certificate & Award Recipients
      - Past Recipients
    - Visitor & Safety Information
  - Changemakers
- Diversity, Equity & Inclusion
  - DEI Report
    - See the Current DEI Report
    - Supporting Data
  - Voices
  - Share Your Thoughts
- Learning at Stanford GSB
  - Overview of Learning at Stanford GSB
  - Faculty
    - Overview of Faculty
    - Teaching Approach
  - Experiential Learning
    - Overview of Experiential Learning
    - Action Learning Program
    - Real-Time Analysis and Investment Lab
  - Guest Speakers
    - Overview of Guest Speakers
    - View From The Top
  - Entrepreneurship
    - Overview of Entrepreneurship
    - Entrepreneurship Courses
    - Beyond the Classroom
    - The Five Lenses of Entrepreneurship
  - Leadership
    - Overview of Leadership
    - Leadership Labs
    - Executive Challenge
    - Arbuckle Leadership Fellows Program
    - Interpersonal Dynamics
      - Overview of Interpersonal Dynamics
      - Facilitation Training Program
        
        Overview of Facilitation Training Program
        
        2024–25 Program
        
        Selection Process
        
        Training Schedule
        
        Time Commitment
        
        Learning Expectations
        
        Post-Training Opportunities
        
        Faculty
        
        Who Should Apply
        
        Introductory T-Groups
        
        Contact
    - Leadership for Society Program
  - Social Innovation
    - Overview of Social Innovation
    - Curriculum
    - Certificate
    - Fellowships
      - Overview of Fellowships
      - Stanford Impact Leader Prizes
      - Impact Design Immersion Fellowship
        
        Overview of the Impact Design Immersion Fellowship
        
        2022 Awardees
        
        2021 Awardees
        
        2020 Awardees
        
        2019 Awardees
        
        2018 Awardees
      - Stanford Impact Founder Fellowships and Prizes
      - Social Management Immersion Fund
    - Experiential Learning
    - Impact Journeys
  - Communication
- Life at Stanford GSB
  - Overview of Life at Stanford GSB
  - Collaborative Environment
  - Activities & Organizations
  - Student Services
  - Housing Options
    - Overview of Housing Options
    - Stanford GSB Residences
  - International Students
  - Our Campus
  - California & the Bay Area
- Voices of Stanford GSB
The Programs
- See All Programs
- MBA Program
  - Overview of the Stanford MBA Program
  - Why Stanford MBA
  - Academic Experience
    - Overview of the Academic Experience
    - Curriculum
    - Global Experiences
    - Faculty
    - Joint & Dual Degrees
    - Academic Calendar
  - Student Life & Community
    - Overview of Student Life
    - Clubs & Activities
    - Diversity
    - Student Support
    - Residential Life
    - Student Voices
    - Alumni Community
      - Overview of Alumni Community
      - MBA Alumni Voices
    - A Week in the Life
  - Career Impact
  - Tuition & Financial Aid
  - Admission
    - Overview of Admission
    - Evaluation Criteria
    - Deadlines
    - Application
    - Interviews
    - Deferred Enrollment
    - Joint & Dual Degrees
    - Entering Class Profile
    - Admission Events
      - See All Types of Events
      - Event Schedule
  - New & Noteworthy
  - Contact
    - View Contact Information
    - Ask a Question
- MSx Program
  - Overview of the Stanford MSx Program
  - Why Stanford MSx
    - See Why Stanford MSx
    - Is MSx Right for You?
    - Career Impact
      - See Career Impact
      - Career Support
    - Alumni Voices
  - Curriculum
  - Admission
    - Overview of Admission
    - Admission Events
    - Evaluation Criteria
    - Application Requirements
      - Overview of the Application Requirements
      - Personal Information
      - Education
      - Professional Experience
      - Reference Letters
        
        Overview of Reference Letters
        
        Information for Recommenders
      - Graduate Tests
        
        Overview of Graduate Tests
        
        GMAT, GRE & EA
        
        English Proficiency Tests
      - Essays
    - Interviews
    - After You’re Admitted
    - Entering Class Profile
  - Student & Family Life
    - Overview of Student & Family Life
    - Student Life
    - Partners & Families
    - Housing
    - Daycare, Schools & Camps
  - Tuition & Financial Aid
  - Contact
- PhD Program
  - Overview of the PhD Program
  - Fields of Study
    - Overview of Our Fields of Study
    - Accounting
      - Overview of Accounting
      - Requirements
    - Economic Analysis & Policy
      - Overview of Economic Analysis & Policy
      - Requirements
    - Finance
      - Overview of Finance
      - Requirements
    - Marketing
    - Operations, Information & Technology
      - Overview of Operations, Information & Technology
      - Requirements
    - Organizational Behavior
    - Political Economics
      - Overview of Political Economics
      - Requirements
  - Academic Experience
    - Overview of the Academic Experience
    - Degree Requirements
    - Faculty
    - Current Students
    - Research Resources
  - Admission
    - Overview of Admission
    - What We Look For
      - Overview of What We Look For
      - Entering Class Profile
    - Application Materials
    - Deadline & Decisions
    - Admission Events
      - All Admission Events
      - IDDEAS
  - Financial Aid
  - Student Life
    - Overview of Student Life
    - Voices
  - Placement
  - Contact the PhD Program
    - View Contact Information
    - Stay in Touch
- Research Fellows Program
  - Overview of Research Fellows
  - Research Community
  - Academic Experience
    - Overview of Academic Experience
    - Standard Track
    - Dedicated Track
      - Overview of Dedicated Track
      - Projects
  - Fellowship & Benefits
  - Admission
    - Overview of Admission
    - International Applicants
  - Contact
Executive Education
- Overview of Executive Education
- Programs for Individuals
  - Overview of Individual Programs
  - On-Demand Online Courses
    - Group Enrollment
- Programs for Organizations
  - Custom Programs
    - Program Formats
    - Developing a Program
  - Catalyst Online Programs
  - Contact Client Services
- The Difference
  - Academic Experience
    - Faculty
  - Campus Experience
    - Executive Dining
    - Executive Residences
  - Live Online Experience
  - Silicon Valley & Bay Area
  - Digital Credentials
  - Faculty Spotlights
  - Participant Spotlights
  - Voices
- Admission
  - Eligibility
  - International Participants
  - Application Process
  - Payment & Cancellation
    - Discounts
  - COVID-19 Updates
- Contact
Faculty & Research
- Overview of Faculty & Research
- Faculty
  - All Faculty Profiles
  - Academic Areas
  - Awards & Honors
  - Seminars
  - Conferences
    - Overview of Conferences
    - Accounting Summer Camp
    - Big-Data Initiative in Intl. Macro-Finance
    - California Econometrics Conference
    - California School Conference
    - Initiative on Business and Environmental Sustainability
    - Junior Faculty Workshop on Financial Regulation and Banking
    - Ken Singleton Celebration
    - Quantitative Marketing PhD Alumni Conference
    - Rising Scholars Conference
      - Agenda
      - Presentations
    - Theory and Inference in Accounting Research
  - Voices
- Publications
- Books
- Working Papers
- Case Studies
- Research Labs & Initiatives
  - Overview of Centers & Research Initiatives
  - Cities, Housing & Society Lab
  - Computational Marketing Lab
    - Faculty & Researchers
    - Research
      - Focus Areas
  - Corporate Governance Research Initiative
  - Corporations and Society Initiative
    - Overview of Corporations and Society Initiative
  - Energy Business Innovations
  - Golub Capital Social Impact Lab
    - Overview of Corporate Governance Research Initiative
    - Who We Are
      - Researchers & Students
      - Funders
    - Our Research
      - Research Approach
      - Publications
      - Domain Areas
        
        Charitable Giving
        
        Education
        
        Financial Health
        
        Government Services
        
        Health
        
        Worker Training
      - Methods
        
        AI & Machine Learning
        
        Short Course
        
        Adaptive & Iterative Experimentation
        
        Incentive Design
        
        Social Sciences & Behavioral Nudges
      - Bandit Experiment Application
    - Conferences & Events
    - Get Involved
    - Contact
  - Policy and Innovation Initiative
  - Stanford Latino Entrepreneurship Initiative
  - Value Chain Innovation Initiative
    - Overview of Value Chain Innovation Initiative
    - Research
    - Faculty & Staff
    - Events
    - Contact
      - View Contact Information
      - Subscribe
  - Venture Capital Initiative
    - Overview of Venture Capital Initiative
    - Contact the Venture Capital Initiative
- Behavioral Lab
  - Overview of Behavioral Lab
  - Conduct Research
  - Participate in a Study
  - Faculty
  - Publications
  - Lab Staff
  - Contact
- Data, Analytics, and Research Computing
Stanford Seed
- About Seed
  - Overview of Seed
  - Leadership
  - Founding Donors
  - Contact
    - View Contact Information
    - Location Information
- Stanford Seed Programs
  - Seed Transformation Program
  - Seed Spark Program
- Companies & Leaders
  - Meet Seed Entrepreneurs
    - Entrepreneur Profiles
    - Company Spotlights
  - Seed Transformation Network
- Get Involved
  - Overview of Getting Involved
  - Coach
  - Consult
  - Intern
  - Collaborate
  - Give
- Discover Impact
  - Overview of Impact
  - Research & Studies
    - Overview of Research
    - Research Library
- News & Insights
  - Overview of News & Insights
- Program Contacts
Library
- Overview of the Library
- Research Resources
- Research Support
- Services
  - Overview of Services
  - Research Data Services
  - Course Support
    - Course Reserves
      - Request Form
    - Course Research Guides
  - Borrow, Renew, Return
  - Print & Scan
  - MBA & MSx Students
  - PhD Students
  - Other Stanford Students
  - Faculty
    - Overview of Faculty
  - Faculty Assistants
  - Research Assistants
  - Stanford GSB Alumni
- Stanford GSB Archive
  - Overview of the Stanford GSB Archive
  - Telling Our Story
- About Us
  - Overview about Us
  - Staff Directory
  - Hours
  - Library Spaces
    - Overview of Library Spaces
    - By Floor
  - Visit
  - History
Alumni
- Alumni Site Help
- Communities
  - Overview of Communities
  - Digital Communities & Tools
    - Overview of The Alumni Network
  - Women’s Programs
    - Overview of Women’s Programs
    - Women’s Circles
    - Stanford Women on Boards Initiative
    - Alumnae Spotlights
    - Insights & Research
  - Regional Chapters
  - Identity Chapters
  - Interest Groups
  - Recent Alumni
- News
- Reunions
  - Overview of Reunions
  - Alumni Day
  - Half-Century Club
  - Plan Your Visit
  - Reunion Highlights
- Events
- Career Resources
  - Overview of Career Resources
  - Job Search Resources
    - All Job Search Resources
    - Executive Recruiters
    - Interviewing
    - Job Boards
    - LinkedIn
    - Negotiating
    - Networking
    - Resumes & Cover Letters
      - Overview of Resumes & Cover Letters
    - Self-Assessment
  - Career Coaching
    - Overview of Career Coaching
    - Long-Term Career & Executive Coaches
    - Complimentary Coaching
  - Career & Life Transitions
  - Programs
  - Career Video Library
  - Contact
- Alumni Education
  - Overview of Alumni Education
  - Research Resources
    - Overview of Research Resources
    - Library Databases
- Volunteering
  - Overview of Volunteering
  - Academics & Student Life
    - Overview of Academics & Student Life
    - Student Clubs
      - Overview of Student Clubs
    - Entrepreneurial Students
  - Admissions
  - Advisory Boards
    - Stanford GSB Trust
  - Alumni Community
  - Alumni Consulting Team Volunteers
    - Overview of Alumni Consulting Team Volunteers
    - Volunteering Opportunities
      - Overview of Volunteering Opportunities
      - How to Volunteer
      - About ACT Projects
      - ACT Volunteers by Class Year
        
        Overview of ACT Volunteers by Class Year
        
        2020 – 2029
        
        2010 – 2019
        
        2000 – 2009
        
        1990 – 1999
        
        1980 – 1989
        
        1970 – 1979
        
        1960 – 1969
        
        1950 – 1959
        
        1940 – 1949
    - Projects
      - Overview of ACT Projects
      - Service Areas
    - Stories & History
    - Leadership
    - Contact ACT
  - Business & Nonprofit Communities
  - Reunion Volunteers
- Giving
  - Overview of Giving
  - Impact of Giving
  - Business School Fund
  - Planned Giving
  - Strategic Initiatives
  - Donor Recognition
    - Overview of Donor Recognition
    - Giving News & Stories
  - How to Make a Gift
    - Overview of How to Make a Gift
    - Giving Deadlines
  - Contact the Development Office
    - View Contact Information
    - Development Staff
- Contact
  - View Contact Information
  - Staff Directory
  - Submit Class Notes
  - Class Secretaries
  - Stanford GSB Alumni Association
Insights
Stanford Business Podcasts
Stanford Business Magazine
- See the Current Issue
- All Issues
  - See All Issues
  - Spring 2022
  - Autumn 2020
  - Catalyst
  - Fall 2021
  - Shift
  - Spring 2021
  - Summer 2020
  - Value
  - Winter 2020
Newsroom
- Overview of the Newsroom
- For Journalists
- School News
- In the Media
  - COVID-19 Analysis
- Contact
Events
Companies, Organizations, & Recruiters
- Overview of Companies, Organizations, & Recruiters
- Recruit Stanford GSB Talent
  - Overview of Recruiting Stanford GSB Talent
  - Post Jobs
  - Interview Candidates
  - Host Events
  - Search for Candidates
  - Strategies & Resources
    - Overview of Strategies & Resources
    - Think Globally
    - Recruiting Calendar
    - Recruiting Policies
    - Employment Reports
  - Contact
- Leverage Stanford GSB Expertise
  - Overview of Leveraging Stanford GSB Talent
  - Internships & Experiential Programs
  - Alumni Consulting Team for Nonprofits
    - Overview of Alumni Consulting Team for Nonprofits
    - Services
    - Clients
    - Working with ACT
    - Contact ACT
      - View Contact Information
      - ACT Leadership
  - Social Innovation & Nonprofit Management Resources
- Develop Your Organization’s Talent
- Invest in Stanford GSB
Stanford Community Resources
- Non-GSB Registration
  - Home
  - Stanford Students
    - Exams
    - Forms
    - Grades
  - DCI Fellows
  - Other Auditors
  - Academic Calendar & Deadlines
  - Attendance
  - Course Materials
  - Frequently Asked Questions
- Overview of Stanford Community
- Entrepreneurial Resources
  - Overview of Entrepreneurial Resources
- Plan an Event
Jobs
- Overview of Jobs
- Faculty Recruiting
- Postdoctoral Positions
  - Overview of Postdoctoral Positions
Visit Us
Contact Us