Jane nd Calvin r tngrs, bth f whm hv mnthl llwn f 100$. Thr r nl tw things tht mttr t thm: hving dt ss n thir phn nd shing fr stuff. Mdl th rblm s hi btwn tw gds, dt nd stuff, with quntit f dt n th hrizntl xis (in mgbts ()) nd quntit f stuff n th vrtil xis. ssum tht bth Jns nd lvins rfrns stisf ur stndrd ssumtins. Sus tht th ri f stuff is $1 r unit. Th ll ll-hn srvi rvidr ffrs tw dt lns. Undr ln , th y s u g ln, th ri r f dt is $0,5 fr vr f dt usd. Undr ln , th mnthl subsritin ln, thr is fid mnthl f f 25$, nd th ri r f dt is 0$ fr th first 100 usd in mnth but 3$ r fr h f dt ftr 100.

. Drw digrm with th budgt nstrint (givn llwn f 100$) undr ln . Mk sur t indit n th xs th quntitis t th intrts.

b. n th sm digrm s th rvius qustin, drw th budgt nstrint undr ln . k sur t indit n th xs th quntitis t th intrts. th Jane nd alvin timiz thir hi f snding f thir mnthl llwn s tht th gt bundl th mst rfr mngst ths th n ffrd. In rtiulr, th n chs whih dt ln t us, ln r .

Sus alvin timll hss t us ln .

. n ur rvius digrm, drw ssibl indiffrn urv nd timl bundl tht is nsistnt with this infrmtin nd lbl it I^alvin.

d. Wh is it likl tht alvins timl nsumtin f dt is 100 r mnth?

. Dmnstrt, mthmtill, tht th budgt frntirs f ln nd ln intrst t th bundls (50 ,75) nd (110 ,45). rk ths intrstin ints n ur budgt digrm.

Sus Jane timll hss t us ln .

f. mining ur budgt digrm, lin wh it must b th se tht Jn is ithr 'hv' dt usr (vr 110 r mnth) r 'light' dt usr (undr 50 r mnth).

g. n ur rvius digrm drw ssibl indiffrn urv nd timl bundl tht is nsistnt with th infrmtin tht Jane is 'light' dt usr.