Answer:
The number of CDs = 111.36
The number of movie videos = 242.72
N/B: I choose not to round up the answers.
Explanation:
The method used is the Lagrangian method. Basically, the optimization problem we are trying to solve is the utility function
subject to the constraint
.
So the optimization problem(Lagrangian) is
,
where is a constant called the Lagrange multiplier.
To find the optimal consumption, we need to maximize the Lagrangian with respect to the variables . This we do by differentiating
with respect to each variable and then equate to 0.
Equate (1) and (2), to get and substitute into (3) to get
. Substituting
into
to get the corresponding value of
.