Quantitative Methods

p" l-n rhe ou

rnodels of rninicomputers. the Alpha ;l and

for in the furniture. the next production 1,200 hours of Iabor are available under a

agreement. The firm also has a stock of 3.500 feet of good-quality r-edw.clod. Each bench that

Outdoor Furniture produc:es requires 4 Iabor hour:s and I 0 board fcct of rcdwood: cach picnic table takes 6 labor hours and 3-5 hoard feet of redwood. Completed benches will yield a profit o{ 59 each. and tables will result in a pr.ofit of g20 each. How many benches and tables should Outdoor Furnirure produce to obtain the largest possiblc profit.l Use the

LP approach. The dean o1'the Western Colle-se of Business must plan the school's course offerings fbr.the lall sentes_ l.er. Student demands rnake it necessary to offer al. Ieast 30 undergraduate and 20 gradr:ate c:ourses in thc tcrm. Iraculty c0lttracts als() dictate that at least 60 courses be offered in total. Each undergradu- ate course taught costs thc college an average ol 52,500 in taculty wages, antl eaeh rrrduur. .,.,urr" costs $3,000. How many undersraduate and gradu_ ate courses should be taught in thc lall so that total

salaries are kept to a mininrum? MSA ComputeftoTltEf nutactures

long as a rettun of atleast 8Vo late this as an LP problem and

irr order to lulfill a contract. AIso, duc to an oversup- ply ol'fans in rhc preccding period, a linrit should be placed on the total numher ol,fans produced. (a) If Electrocomp decidcs that ar least 20 air con-

ditioners should be produced but no more (harr 80 Ians should bc produced, what would be thc optimal solution'l How much slack or surplus is thcre for each of the fbur constraints',)

(b) Il Elecrrocomp decides that at least 30 air con_ ditioners should be produced but no more than 50 fans should be produced. what woulti be thc optimal solution? How much slack or surplus is there for each of the four constraints at the opti- mal solutron'l

mayor tn a town has

ad costs and reaches an 7,000 peo-

paign would 1 reach as manv people that at ieast 10 ads

any ads of each typc should bc used? How will this reach?

DtscusstoN QUEST|ONS AND pRoBLEMS 291

wants to see at

-5s produced

_qenerate li 1,200 unit. and Bera 5s yielil $1,800 each. Dere thc most prolitablc numbcr of each model of m r to produce during the coming month.

7-20 A winner o{'the $50,000 per

. Although a goal is to get the possible some consideration is given to dex on ls atssl Io each o{'the two stocks. 'l'he total risk

portIolio is found by nrultiplying rhc r.isk ot stock by the dollars invested in that stock.

Thc lirllowin-e table provides a summary ol'the m and risk:

STOCK ESTIMATEDRETURN RISKINDEX Putrochemical

Lttitiry 12Vc

6c/o

9

4

The investor would li to maximize the return on thc investment. but the risk index of the in-

than 6. How muchvestment should not be should bc investcd in each k? What is rhe aver- agc risk fbr this investmcnt? r-eturn fur this investment?

pz7-zr Relerring to the 'fex as L0tto si i 7-20,.11 s aboutsupposc the invcstor has changcd a

the invcstment and wishes t.r sive' tcr empha- sis to the risk of the investrnent. N the irlvestor u,ishes to minimize the risk of t nt as

is thc esti

. Formu- the jrnal sitlu-

Q:7-r8

$e 7-?2 Solve the following problem using the point graphical met culatc the slack for.

. At the optimal solution, cal-

tion. Hou,,rnuch should be i ted in stock'? What is the average risk thcr cstinratcd return lbr

constraint:

Marimize

subject to

invcslmcn[ ?

:4X + 4Y 3x+-5y=150 x-2Y<1A

5X+3y<150 X,Y > O

tw() the

Beta -5. The llrm enrploys live tcchnicians, work- ing 160 hours each pcr rnont.h, on its assembly linc. Managemenl insists that Illl employm er"tt (t.t.. ctll 160 hours of time) be maintained ffr each worker during next moTrh's operations. Iy'equires 2O labor hours ro asser{ble each Alplfi 4 compurer and 25 labor hours r{assemble eagfi Beta 5 model. MSA

$40,000 for lasr-minure advertising in the clays pre- ccding tLrc elcction. Two typcs of a<Js will bc used: radio {nd tclevision. Each ladio ad costs $200 and reecht--s\an esrilnared -3.000 peoplc. Each telcvision

,rf cach type m\t tleulsc,.t. Also. the number of raclio ads must hc at l\st'us -qreat as thc number ol'Lelc_

FurnitL\e Corporation manu lacturcs . hcnchts \nd picrric tirhle s. lirr. usc in

parks. Thc lir\ has trvo pn j11 rt'sourcc\. tluhor lbrcci\nd a supply trl retJwood

x-2Y<1A

Qua,titative Anatysis for Managemed, Twerfth Edition, by Barry Render, Rarph M. stair, Michaer ECopyright O 201 5 by pearson Education, lnc. Hanna, and Trevor S. Hale. publjshed by prentice Hall.

fri:7-16 A

ple. In

period. Alplra 4s

has decided ro invest