Utility Function Problems

Hi, I’m having a lot of trouble with this question as I just can’t seem to figure out the value of Px, if it is at all possible to figure out Px, and I’m also having trouble answering the other questions. It would be great if someone could offer some help or work me through the questions. Thanks.

3. Suppose that you have the following utility function: U(x,y)=6x^0.5+y.The price of x is Px and the price of y is 1.

a. Your income is Y = $24. Find the uncompensated demand for good x. That is, find the amount of x which maximizes the consumer’s utility, subject to affordability. You can use any method you want. Do not worry about corner solutions.

b. What is the income elasticity of uncompensated demand for good x?

c. Now suppose that you want to attain utility U = 10. Find the compensated demand for good x. That is, find the amount of x which minimizes your expenditure, subject to attaining utility of 10. You can use any method you want. Do not worry about corner solutions