Suppose April has the following quasilinear utility function from soda x and other stuff M: U(x, M) = 10 x + M. The price per unit of soda is $p, and the price of other stuff is $2 per unit. April has an income of Y = 100. Assume that soda is a continuous good.

 Assuming an interior solution, show that April's optimal quantity of x is x  = 100 p2 . Explain why p must be great than 2 for the optimum to be interior