Question

Maurice has the following utility function: U (X Y) =20X+80Y-X^2-2Y^2, where X is his consumption of CDs with a price of ​$11 and Y is his consumption of movie​ videos, with a rental price of ​$2. He plans to spend ​$50 on both forms of entertainment. Determine the number of CDs and video rentals that will maximize​ Maurice's utility.

Answer 1

1 CD and 19 movie videos

Step-by-step explanation:

This is a quadratic programming problem. Given the utility function, product price and budget constraint. the following relation between X and Y is:

`Y =(50-11X)/(2)`

When that is inserted in the utility function, the function is:

`U(X) = -X^(2) -420X+200-(121X^(2)-1100X+2500 )/(2)`

In order to find the maximization parameter X, the first derivative of the function is needed (leveled with zero), and it is:

`-123X + 130 = 0`

The value for X is 1,06 which can be rounded to 1. From the first relation, we see that Y is 19.