Alice's utility function is given by (U (x, y) = ln(x) + ln(y), where x and y denote the quantities of pomegranates and grapes Alice eats.

Alice's utility function is given by (U (x, y) = ln(x) + ln(y), where x and y denote the quantities of pomegranates and grapes Alice eats. The prices per kg of these two fruits are 10e and 5e respectively. Alice has 400e that wants to spend fully on buying these two fruits.

(a) Find the quantities of pomegranates and grapes that Alice should get to maximise her utility.

(b) Approximate the quantities she should buy if she had 403e to spend.