In Manifold, Missouri (pop. 1,000), people all have the same tastes and they all like Buicks. Nobody wants more than one Buick, but a person with income $M is willing to pay about $.10M per year to have a Buick. Nobody in Manifold has an income greater than $50,000 and nobody has an income less than $10,000. For incomes, $M, between $10,000 and $50,000, the number of people with incomes greater than $M is about 1,250 - .025M. If it costs $2,000 a year to have a Buick, how many people in Manifold will demand Buicks?

Question

Quizplus · Accepted Answer

First, we need to find out the income range of the people in Manifold who are willing to pay for a Buick. Since nobody wants to spend more than $.10M per year on a Buick, we set up an inequality:

$2,000 ≤ .10M

Solving for M, we get M ≥ $20,000. Therefore, only people with incomes greater than or equal to $20,000 will demand Buicks.

To find out how many people in Manifold have incomes greater than or equal to $20,000, we need to substitute M = $20,000 into the given formula:

1,250 - .025M ≥ 1,250 - .025($20,000) = 750

This means that there are 750 people in Manifold with incomes greater than or equal to $20,000. Since we know that everyone in Manifold likes Buicks, we can safely assume that all 750 of these people will demand Buicks.

Therefore, the correct choice is B) 750.

In Manifold, Missouri (Pop