Quantitative Methods

a

Re"na.cnder orD QuUlJtort 8'Q 316 CHAPTER 8 . LINEAR PROGRAMMING APPLTCATIONS

and newspaper ads. The costs of these, the audience reached by each type of ad, and the maximum num- ber available is shown in the following table:

manufacturer is notified by Sundown about the num- ber ofcars needed during the next six months. The automobile manufacturer has stipulated that at least 5O7o of the cars leased during a six-month period must be on the five-month lease. The cost per month on each ofthe three rypes ofleases are $420 for the three-month lease, $400 for the four-month lease, and 5370 for the five-month lease.

Currently, Su has 390 cars. The lease on 120 cars expires at t of March. The lease on

COST

T}?E OFAD PER AD AUDIIINCE MAXIMUM

REACHED/AD NTINIBER

TV

Radio

Billboards

Newspapers

$800

$400

$s00

$1 00

30.000

22,000

24,000

8,000

l0 t0

10

10

ln atldition. Nlartinez has docided tl'rat there should bc at lcast six atls on TV or radio or some com- bination o1'those two. The amount spent on hillhoards and newspapers together must not excecd thc amount

spent on TV ads. While tundraising is still continu- ing. the monthly budget for advertising has been set at

$ 1 5,000. How many ads of each type should be placed to rnaximize the total number of

8-1 (Media selection problem) The advertising director lirr Divcrsey Paint and Supply, a chain of litur retail stores on Chicago's North Sidc, is considering twtt

pa-ec ads in thc Sunday Chit:ago Tribrute and the other is lor advertising time on Chi

ity's neigh- areas.

Use LP to ine lrow many cars shguld be each t,vpe of I ovcr the six- period.

How many cars arl: thc cnd of st?

*: s-s Management of Rent-a-Carr(see Problem 8-8) has decided that the cost/drn-ing the six-

another '140 cars ex lease on the rcst of r

leased in each month mize the cost ol'leasi

month period is not the because the agency may

to determine how many month on each rype of leasing over the entire li

blc for assigning in his county. He

at the end of April, and the se expires at the end of May.

to minimizc to additional

should be leased in each to minimize the cost of

lcascs.

three high schools need to bus a certain

sideration has citv homes and

months on some leases For erample. if Sundown had some cars at the beginning of the sixth month, Sundown still he obligated for two additional months on 1"use. LJ5e: LP

yourself lfl an 8-10 (High school busing r) The Arden County,

Nlaryland. supetin ation is responsi-

37c in the north The newspaper has corresponding of lVa and3Vo pet ati. The cosi oi'a hall'- advertisement is $925; a telcvision spot 000.

Diversev Paint wou ike to select the least costly advertising s cxposurc lcvels.

would meet desired

(b) Solr,e the probl

8-8 (Automobile problem) n Rent-a- Car. a large auto rental operattn,q 1n the Midwest, is next six months. tomobile manu public on a dai basis. A forecast of the demand for Sundown's in the next six months follows:

MONTH MARCH MAY JT'NE JULY AUGUST

42{)

number of srudents,for several of the county are hevond walki distancc to $ schorrl. The suPcr- intendent parti the county i\rtoytue geographic sectors as he minimize the

pts to a plan that will number of miles traveled

by bus. He izes that il $ student happens to lir,e in a ccr(ri n sector and is to the high school in that therc is no neeU to bus that sru- dent because or she can wdk to sthool. The three schools are in sectors B, C. aM E.

The tahle reflects the number of hieh- schrxrl- living in each sector and the bus- lng in miles from each sector to each school:

The TV an L:xposul"e

ng time under per spot of 57o

DIS'IANCE TO SCHOOL

SECTOR

SCHOOL IN SCHOOL IN SECTORB SECTORC

SCHOOLIN NUMBERO}' SECTORE STUDENTS

700

-5(Xl

100

tt(x)

400

440170

A

B

C

D

E,

5

0

4

7

t2

8

1

0

2

7

6

12

1

5

0

Cars may be leased from the nianufacturer for either thlee, Ibur. or five months. These arc leascd on the frrst day of the month and are returned on the last day of the month. Every six months the automobile

Stair, Michael E. Hanna, and Trevor S. Hale. Published by Prentice Hall. Copyright @ 201 5 by Pearson Education, lnc.

) 5{)0

exposrlre le\l of at least ;l0ol: within borhoods andYO? in northwcst

undown lc-ases carYfroffl an au- and then rents them to the

[)cmand

Quantitative Analysis for Managemeni, Twelfth Edition, by Barry Render, Ralph M

(a) Formulate using

media possibilities. Onc plan is lirr a

The storcs are expanding