1 Instructions for Case - Introduction: What is the case, and what is the problim? - Idens/Conclusions Condude yomr wark with your ideas on the case-(Amalyat the result of nach constraint and maloe stiggetions acoutuling to thrse resalte) - Referencen Put evry source you ased in refirmous nven if yoe dal not sse it for cilaticme - Appendix: Fut every calculatica you did to solve questions in the appendix. Mdd screcmebots ef the "solver" part. Prepare in rejort fornat. (Do aot fonget to include the cover page and table of coadents. Frase coedider the them with the muruaibet and name of the group suetabss. (For instaboe, if group memibers ane Gerae Summos and Paul Stanky, they will save their files as "Simmons, Geac atd Staniry, Patl") 2 Premier Protein Company Case Premicr Protrin Company is a food and bewrae mandfartierct 1hat speriakins in peodaciag autritional drinks. They are currently develoging a new pecteis shake that requirs blrnding four differnat ingerelieste whey proteis coscrutrate, maltoolextrin, cocoe powoler, ad vasilla eatrart. The goel is fo prodore a bigh-protrin whake that taster great ahat is coet-eflective to jrooluce. Howove, Premier Protetn Cotmpany fwos arveral challerggs with that bhruling jroome. Theg hase limbed to various conntraints, sach as the macimtun athd mintmum peroctitages of each ingredicet that can be ased in the final prodect, and the total guantity of the final jeoluct that nevib to be frodared. To address theme challengrs, Pretaicr Protein Cotapaiy has docided to aw miard luteger lenar peugaamage to develop a model that will belp thrm deternise the optimal blend of ingredients to nee in their pecoein ahaler. The randel wall take into uccostht the quautitios atal conts of rarh ingendirst, an well as the dremed tatritional and tase characteristics of the final product. Premier Protestu Couppaiy bas determined that thry ueed to jeoduce 1000 liters af thrir arw peokrut shales. This quantity represcrts the total anoount of the find peiduct that they novel to jooduce in orker to awet their curreat demand. Veing the nixod integer linear focograuming model, Freminr Frotein Cokipasy will be able so money in the production process, While also emsuring that the final prodact movts their erality abd amtritioeal matalaris. Table it Available ingredirats for blending Cocio flavor intensity and vanilla flavor imtensity are impartaat parnmeters to consbler wben bisding ingredistitn for food products, In thas case, the cocen thaver intemaity rasgos frum 3 ao 6 eat a satir of 1 to 10, which meass that the bledded peoduct shesald havw a moderately stroag cocoa flivie, Similagly, the vanilla Havor irtenaity tanges froen 2 to 4 on the same scale, ibdicating that the pruchort should lave a mill to moderate vailla flavir. By kaveping throe flaver inteneity rasges in mind, the food masudarfure cas crote a jrediat that satisfies custuener prrferences asd ases their quality standards. The goul of Premiet Protein Coupuay Compary is to minimize bending ecet. (Please convider each equestiou wparately, Accept sction "B' as a Dase Case aud anotify the changes you enake to each option haved on this soenario. For example, do sot ves the changes you make to the constraints sccorating to the directions in section C in the following options.) a) Write decision variahles of the case in detall and specify objoctive fuaction (miniaization of Preasier Proteia Coupary blendiag cost) and coustraists at a matheinatical model. (You can fiod the example foe the mathimatical model below; ) The variahles ane definnd as x1=sumberofall-ilktiesproducedpermonthx1=numberofpolyentertiesx3=numberofblendIpoly-coetiontiesx4=numberofbiend2silk-eceineties subject io Maimiseprofic=516.24x3+58.22x2+58.77x3+58.06x40.125x1+0.06x11.200(yandsofsik)0.05x2+0.06x13000(yandsofpobester)0.05x3+0.044x21.00(yardiofcothos)x15000(contractminimumforallsilk)x1700(comeractmaximum) b) The minimization of coot ls the objextive of Pretaine Protein Ccanjany for this product, Please find hove chany litres of each product type should be used foe the blend to be peodusce. (Plense indicate cont minimization polbt abd use solver as solution methodology; Assume that the decision variables of the case are integers.) e) Deu to anforisees circumstances. Premier Prutein Coxpaciy's semand for the blended product has dropped, and they nos sed to produce caly 850 Liters of the product. As a fosth, the exbstiag blended produet ogtimization model beris to be moditied to emsure that the production plas ks opimizd for the new podaction qiastity. d) In order to cotmply with health regulations, Premier Protein Coatpayy Euast ase Npecific perceztapes of ech iggredient in their proteis shaloe. The allowable nugges for each ingredient are as follows: This table shows the allowable peromtage runges foe earh ingredient in Prember Froteit Compuryy's protein shake, By incorporating these constraists into their mixod isteger lineng programming model, they can opkitnibe coapoany's ingredicut blead to exatre that the fimal protust mects thrir quality aad autritional standarda, while uleo complying with bealth regulations. e) Premier Protein Cotupany bas set a minimam requiremaent for the ptodein coutest in tbeir protrin shake, with a target of 20 gramk of protein per liter of the final prodict. This target has been set to meve the tutritional standards and cpiality tequirements of their ptoduct, as well as to appoal to constunets who are booking for high-protein nutritional drinks. In their marketing efforts, the compauy can use this information to highlight the prutein contert of their product, whind may belp to differentiate it from other protein shakes on the market. f) Preasier Proteis Compaty lans rexmatly esjerirsend a siguificant increase in the atapply of inpat itgreetients for the blemded product. However, due to the limitted caparity of their production farilitim, they ean no lotiger use the entire availahle zuatitity of earfu leput ingredient in their ptodinetine plaali. The apdated availahle contents are as listave in the taluk