Question

Antonio has $11.00 to spend on a lunch consisting of hamburgers ($1.50 each) and French fries ($1.00 per order). Antonio's satisfaction from eating x1 hamburgers and x2 orders of French fries is measured by a function U(x1, x2) = x1x2 . How much of each type of food should he purchase to maximize his satisfaction? (Assume that fractional amounts of each food can be purchased.)

Answer 1

Answer: $4. 71 hamburger and $6.29 French fries.

Explanation:

Total spendable income of Antonio = $11.00  

1 hamburger = $1.50

1 order of French fries = $1.00

Utility maximization function: U(x1, x2) = x1x2 i.e. 1 hamburger and 2 orders of French fries

Using the Utility maximization function: U(x1, x2) = $1.50 + $2.00

                                                                                      = $3.50 per lunch  

Therefore the customer will purchase hamburger worth of $(1.50 x 11.00/3.50) = $4. 71

And French fries orders worth of $(2.00 x 11.00/3.50) = $6.29

Antonio will maximize his satisfaction by purchasing $4. 71 hamburger and $6.29 French fries.