The political pollster Canter is preparing for a national election. It would like to poll at least 2,400 Democrats and 2,400 Republicans. Each mailing to the East Coast gets responses from 100 Democrats and 50 Republicans. Each mailing to the Midwest gets responses from 100 Democrats and 100 Republicans. And each mailing to the West Coast gets responses from 50 Democrats and 100 Republicans. Mailings to the East Coast cost $40 each to produce and mail, mailings to the Midwest cost $60 each, and mailings to the West Coast cost $50 each. How many mailings should Canter send to each area of the country to get the responses it needs at the least possible cost What will it cost ?
A)16 mailings to the East Coast, none to the Midwest, 16 to the West Coast, the cost is $1,440
B) No mailings to the East Coast, 24 to the Midwest, none to the West Coast, the cost is $1,440
C) 24 mailings to the East Coast, none to the Midwest, 24 to the West Coast, another solution resulting in the same cost is no mailings to the East Coast, 16 to the Midwest, none to the West Coast, the cost is $1,440
D) 16 mailings to the East Coast, none to the Midwest, 16 to the West Coast, another solution resulting in the same cost is no mailings to the East Coast, 24 to the Midwest, none to the West Coast, the cost is $1,440
E) No mailings to the East Coast, 16 to the Midwest, none to the West Coast, the cost is $1,440

Question

The political pollster Canter is preparing for a national election. It would like to poll at least 2,400 Democrats and 2,400 Republicans. Each mailing to the East Coast gets responses from 100 Democrats and 50 Republicans. Each mailing to the Midwest gets responses from 100 Democrats and 100 Republicans. And each mailing to the West Coast gets responses from 50 Democrats and 100 Republicans. Mailings to the East Coast cost $40 each to produce and mail, mailings to the Midwest cost $60 each, and mailings to the West Coast cost $50 each. How many mailings should Canter send to each area of the country to get the responses it needs at the least possible cost  What will it cost  ?
A)16 mailings to the East Coast, none to the Midwest, 16 to the West Coast, the cost is $1,440
B) No mailings to the East Coast, 24 to the Midwest, none to the West Coast, the cost is $1,440
C) 24 mailings to the East Coast, none to the Midwest, 24 to the West Coast, another solution resulting in the same cost is no mailings to the East Coast, 16 to the Midwest, none to the West Coast, the cost is $1,440
D) 16 mailings to the East Coast, none to the Midwest, 16 to the West Coast, another solution resulting in the same cost is no mailings to the East Coast, 24 to the Midwest, none to the West Coast, the cost is $1,440
E) No mailings to the East Coast, 16 to the Midwest, none to the West Coast, the cost is $1,440

Quizplus · Accepted Answer

To minimize cost while meeting the requirement of at least 2,400 Democrats and 2,400 Republicans, we can calculate the cost and number of mailings for each scenario. Sending 16 mailings to the East Coast and 16 to the West Coast yields 2,400 Democrats and 2,400 Republicans at a cost of $1,440. Alternatively, sending 24 mailings to the Midwest also meets the requirements with the same cost of $1,440, showing that both strategies are equally cost-effective.

The Political Pollster Canter Is Preparing for a National Election