Business Calculus

Business Calculus

Business Calculus Advanced Application

Lagrange function

This is an example of analysis using the Lagrange function and Excel solver when there cognition of a company can be expressed as a formula. If you're not good at integration, see Excel Solver.

*Market Environment

According to a survey by a market research firm in the beverage industry, the company's awareness (target age: 15 years old and over, under 25 years old: L;) is proportional to the cube of the sales volume of coffee (x) and the product of the sales volume of tea (y).

L= x^3y.

Due to production facility limitations, the maximum sales volume of Z company's coffee and tea for the coming season in this industry is as follows:

x + 2y =16 billion yen.

*Question

What is the combination of coffee (x) and tea (y) sales volumes that maximizes the company's awareness (L)?

*Answer

Using the Lagrange function and the first-order condition...

By solving the above system of three equations,

the values of coffee (x)= 12 billion yen , tea (y) = 2 billion yen, L=3456, which is the maximum.

Alternative solution: Example solution using Excel's solver

We got the same results of above : coffee (x) = 12 billion yen ,tea (y) = 2 billion yen, L=3456, which is the maximum.

A quick note on business calculus : The area of a figure formed by a string of length L

Lagrange function

This is an example of analysis using the Lagrange function and Excel solver when there cognition of a company can be expressed as a formula. If you're not good at integration, see Excel Solver.

*Market Environment

According to a survey by a market research firm in the beverage industry, the company's awareness (target age: 15 years old and over, under 25 years old: L;) is proportional to the cube of the sales volume of coffee (x) and the product of the sales volume of tea (y).

L= x^3y.

Due to production facility limitations, the maximum sales volume of Z company's coffee and tea for the coming season in this industry is as follows:

x + 2y =16 billion yen.

*Question

What is the combination of coffee (x) and tea (y) sales volumes that maximizes the company's awareness (L)?

*Answer

Using the Lagrange function and the first-order condition...

By solving the above system of three equations,

the values of coffee (x)= 12 billion yen , tea (y) = 2 billion yen, L=3456, which is the maximum.

Alternative solution: Example solution using Excel's solver

We got the same results of above : coffee (x) = 12 billion yen ,tea (y) = 2 billion yen, L=3456, which is the maximum.

A quick note on business calculus : The area of a figure formed by a string of length L