An individual's utility function is represented by: U = X1 ^ 0.9 * X2 ^ 0.1 Their budget constraint is:

An individual's utility function is represented by: U = X1 ^ 0.9 * X2 ^ 0.1

Their budget constraint is: 10,000 = 2X1 + 5X2

That is, their total budget is $10,000 and the price of X1 is $2 and the price of X2 is $5. Use the Lagrangian function to find the optimal values of X1 and X2 that maximises utility subject to the budget constraint[1]. What is the value of l and what is its interpretation?

[1] There is no need to check the second order conditions.