HL Mathematics IA

본 문서는 2018년 5월 아이비 시험을 위해 쓴 HL Mathematics IA입니다. 주제는 라그랑주 승수법 (Lagrange Multiplier)입니다. 만점에 가까운 19/20 점수를 받았습니다 (IB 7).

[본문내용]

Introduction:
After studying Business and Management for the past two years as a part of the IB diploma, and due to
my father being a businessman, I became increasingly interested in how a business can maximize its
efficiency which allows for revenue maximization – a crucial factor in profit maximization, which are the
primary objectives for many businesses. In other words, how businesses can best utilize their scarce and
limited resources in order to maximize their financial benefits.
Moreover, after learning optimization in the differentiation unit in the first year of mathematics in the IB
diploma, I wanted to apply the skill of differentiating a function in order to find the maxima or minima
onto businesses, in order to find the quantities of the inputs (resources) businesses can use to maximize
their revenue, and ultimately, their profits.
After some research, I realized that using just single variable differentiation will not be realistic due to
businesses having multiple resources (this investigation will only analyze two resources) that are often
fixed due to the constraints businesses have in terms of their budget; for example, a business utilizing
labor and steel incur different costs in each resource and have a fixed budget to spend. Initially, I believed
that the utilization of implicit differentiation – the differentiation of an equation with respect to each
variable – would allow me to solve the problem of multiple resources, and hence, multiple variables…

• 과목명: Mathematics
• 주제: 라그랑주 승수법 (Lagrange Multiplier)
• 총 페이지수: 19 pages
• The file is in PDF format.