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 cost of interviewing different types of voters varies due to differences in proportion within the population. the cost of interviewing males, for example, are $10 per democrat, $9 per republican, and $13.50 per independent voter. the costs to interview females are $12, $11, and $13.50 for democrats, republicans, and independents respectively. the polling service has been given certain criteria to which it must adhere.

cost

Males democrat x 10

Republican y 9

independent 13.5

Females democrat w 12

Republican r 11

independent 13.5

x + y + z + w + r + t = 4500

x + y + z ≥ 2000

x + y ≥ 1800

y + r ≥ 1800

w + r + t ≤ 1750

y < 0.25 (y + r)

0.75y < 0.25r

x, y, z, w, r, t > 450

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 republicans 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:

cost

Males democrat x 10 1300 13000

Republican y 9 450 4050

independent 13.5 450 6075

0

Females democrat w 12 500 6000

Republican r 11 1350 14850

independent 13.5 450 6075

4500 50050