Write down the necessary k-t conditions with nonnegativity

Question

Question: (a) Consider the utility maximization problem, maximize x + ln(1 + y) subject to 16x + y ≤ 495, x ≥ 0, y ≥ 0

Write down the necessary K-T conditions (with nonnegativity constraints) for a point (x∗, y∗) to be a solution.

(b) Find the solution to the problem.

(c) Estimate by how much utility will increase if income is increased from 495 to 500.