Problem
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 vary due to the differences in proportion within the population. The costs to interview 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 Democrat, Republican, and Independent voters, respectively. The polling service has been given certain criteria to which it must adhere:
There must be at least 4,500 total interviews.
At least 1,000 independent voters must be polled.
At least 2,000 males must be polled.
At least 1,750 females must be polled.
No more than 40% of those polled may be Democrats.
No more than 40% of those polled may be Republicans.
No more than one-quarter of those polled may be Republican males.
Each of the six categories of voters must be represented in the poll by at least 10% of the total interviews.
Determine the least expensive sampling plan and the total cost to carry out the plan.