# lagrange: Method of Lagrange Multipliers

Exercise template for minimizing a linear objective function with two arguments subject to a Cobb-Douglas-type constraint. Both the parameters of the functions and the exact question (argument 1 vs. argument 2 vs. function value in optimum) are drawn randomly.

**Name:**

`lagrange`

**Type:**

**Description:**

Computing the solution to a cost minimization problem subject to an output constraint where the production fuction with arguments capital and labor is of Cobb-Douglas type. As

`num`

exercises have only a single numeric solution (and to make test takers read the exercise carefully), one of three natural quantities in the optimum is selected randomly as the question: the first argument (capital), the second argument (labor), or the minimal function value (costs). The optimal solution is also displayed graphically using a contour plot.**Solution feedback:**

Yes

**Randomization:**

Random numbers, text blocks, and graphics

**Mathematical notation:**

Yes

**Verbatim R input/output:**

No

**Images:**

Yes

**Other supplements:**

No

*(Note that the HTML output contains mathematical equations in MathML, rendered by MathJax using ‘mathjax = TRUE’. Instead it is also possible to use ‘converter = “pandoc-mathjax”’ so that LaTeX equations are rendered by MathJax directly.)*

**Demo code:**

```
library("exams")
set.seed(403)
exams2html("lagrange.Rmd", mathjax = TRUE)
set.seed(403)
exams2pdf("lagrange.Rmd")
set.seed(403)
exams2html("lagrange.Rnw", mathjax = TRUE)
set.seed(403)
exams2pdf("lagrange.Rnw")
```