# graph of dependent income

I would need help with the following problem about consumer theory. Let us say that $$X$$ is the amount of days at the sea and $$Y$$ is the amount of days on the cottage. We have some utility function $$u(X,Y)$$ and constraint $$4X+9Y=I$$. I have found the optimal solution $$(X^{\star}=\frac{I}{5},Y^{\star}=\frac{I}{3})$$ and I am supposed to graphically illustrate and comment dependence $$X^{\star}$$ and $$Y^{\star}$$ on income $$I$$. I am not sure if i understand exactly the task. Could you help me with the solution? Thank you.

• I feel like X should be the amount of days at the sea and Y should be the amount of days on the cottage and then you should have some some utility function $U(X,Y)$ which you can express with indifference curves. – Bayesian Jan 4 at 13:40
• I have changed the task, would you know now? – Laura Jan 4 at 14:01