A political polling organization is to conduct a poll of lik

A political polling organization is to conduct a poll of likely voters prior to an upcoming election. Each voter is to be interviewed in person. It is known that the costs of interviewing different types of voters varies due to differences in proportion within the population. The costs to interview males, for example are $10 per democrat, $9 per republican, 13.50 independent voter. The cost for females are  $12 per democrat, $11 per republican, 13.50 independent voter. Criteria to which must be adhered:

there must be 4500 voters

100 independent voters

2000 males

1750 females

no more than 40% democrat

no more than 40% republican

no more than 1/4 of those polled republican males

each of the six categories must be represented by at least 10%

Determine the least expensive sampling plan and the cost to carry it out

Solution

z+t =200 As both z and t have same cost let z =t =450

x+y+z>=2000 and x+y >=1800 gives z>200 as z =450 this is satisfied.

As t =100, w+r <=1650

For democrat and republicians males cost is less than females. Hence keep the females to the minimum requirement.

. Take y =450 and r =1350

w= 500, r =1350, t =450

x=1300 y = 450 z=450

OPtimal mix and cost is as follows: