Consider two Bertrand competitors in the market for hipster coffee, Jonas and Kar Yi

Consider two Bertrand competitors in the market for hipster coffee, Jonas and Kar Yi. The coffees of Jonas and Kar Yi are differentiated, with the demand for Jonas’s coffee given by qJ = 30 – pJ + pK, where qJ is the quantity Jonas sells, pJ is the price Jonas charges, and pK is the price charged by Kar Yi. The demand for Kar Yi’s coffee is similarly given by qK = 30 – pK + pJ. Assume the marginal cost of producing coffees is zero for both producers. Find the Bertrand equilibrium prices and quantities as well as the profits for these two competitors.