Exercise 1.3 Suppon that a dewekper hoosing temants for a shopping oter. T'here are for posible tenante a departmmt stom, a toy tore, a shoe stoen, and a hardware store. If each ntore we to be keated in isolation outakde a shopping omter il would earm a certain level of gros profit per period (this the level of peulit befure wattrneting out span rent). In addilkn, ench tore require a certain nber of mpuure foet of foor spae, which i the same ogudles of whether or not it koates in opping onter. The relevant valan for h tare lype a fulkw Gn peolit in impil uam б Ilation Thpartment ta "Tuy stoe She stom IHardwn stor SI00,00 $1,00 $7,N00 17,00 1,000 1,100 Whem the stores are located togther ah stom eamsagenter gm prolit from the additional customer tralle generated by the nearty locations of other stoees. The incree in gom prodi for eh tore type ("alfocted stom type") resulting from the premee of other stoen types ("added tore type") fllw Adll stom lype Shoe Hardware SI00 S00 Afleted stom type Deparimem Thy Shoe Departand Thy вадо $2000 Sидо0 S00 Hantware S00 Suppen that the shopping onter develper chargs a rent egal to ench storels gro prodit, laving the tore with t prolit of atly wm. Tatal wat from the shopping omter un oqual to the tetal gron pelit of ull ita stoe. The devkaper' pealit is ths equal to total gr peolit of all loren in the omter mitn thn eet of peviding paee). Pinally, mppene that, owing to high quality cmtrution and thn ned to provide eummon pan arond the stemm, the constructiom cet for the shupping onter spce in high. In partienlar, mppo thal the ont per perid per squa foot of store foot npe i SI0. (a) Gim an intuitive explanation for the pattern of incremntal proita from the prnoe of other storee in the nd tahle abom. (b) Suppose the dewekper were to contrut a ingle tore shoppingE center (a contrndiction in terms, perhape). There am four types of mch centers (a degartment stom alonn, a tey stom akonn, and so on). Using the information abom, compute the devekopee's peufit from cah of these fer typen of onten. (e) Next comprate the dreloper'n profit from the various typen of twstere shopping centers (le, degartment steen plan nhoe ntoen, department stere plus tey stem, and on, how many pnitilitin are thee) (4) Pinally, eompute prodita form the varkn typen of thren tore mdes and from the singde type f four-tom tew. (e) Comparing your anwem from (b), (e), d d), identily the optimal shopping emter (the cnn yelding the hight penfit to the developer). Kixplain intultively why thi partiealar electim f ste is ptimal.