Aris and Logan share an apartment. They have both been very busy with classes over the past month and the common space has become messy. Aris's parents are coming to visit this weekend and so they've decided it's a good time to clean up. Both Aris and Logan choose how many minutes to clean: XA and XL, respectively. The percentage of common space that they successfully clean depends on how many minutes they clean and is given by the function f(Xa, x) = (1/15)(12XAXL 2(XA + X1)2). Because Aris' parents are coming to visit, he cares a bit more about how clean the space is. His utility is given by UA(XA XL)-(15/2) f (XA X)-30XA - note only the function f is multiplied by 15/2. Logan cares a little less but is also quicker at cleaning His utility is given by UL (Xa, x ) = (15/4) f(XA, X)-15Xp In the Nash equilibrium. how many minutes does each roommate clean? What percentage of the common space do they successfully clean? Please show your work and explain your answers