Jeremy is an economics learner who loves hamburgers. He could eat any number of them for dinner, but he gets a really bad stomach ache after eating a certain amount. In fact, his utility function for hamburgers is given by
where Q is the number of hamburgers he eats for dinner (with Q ≥0).
(a) How many hamburgers can Jeremy eat before he gets a stomach ache (that is, before hisutility becomes negative)?
(b) Determine the optimal number of hamburgers that Jeremy can eat as a function of p, the price per hamburger. (Hint: You have to maximize Jeremy's "net utility". That is, his utility minus the amount he spends on hamburgers.)