Adam and Catherine are choosing between two ice cream shops, Icy and Frosty, located at either end of a 1-mile-long beach. Adam is standing in front of Icy, while Catherine is standing in front of Frosty. Both Adam and Catherine are each willing to pay, at most, $6 for one ice cream cone. It costs them $1 to walk the 1-mile distance between the shops. Icy is government-run, so the price is fixed at exactly $4/cone and will not change. The shops face costs of $0.25/cone. What price should Frosty charge if it is to maximize its total profits from Adam and Catherine?