On a Tropical Island There Are 100 Potential Boat Builders

question 9

Multiple Choice

On a tropical island there are 100 potential boat builders, numbered 1 through 100.Each can build up to 16 boats a year, but anyone who goes into the boatbuilding business has to pay a fixed cost of $15.Marginal costs differ from person to person.Where y denotes the number of boats built per year, boat builder 1 has a total cost function c(y) = 15 + y.Boat builder 2 has a total cost function c(y) =15 +2y, and more generally, for each i, from 1 to 100, boat builder i has a cost function c(y) = 15 + iy.If the price of boats is 40, how many boats will be built per year?

• A)624
• B)200
• C)936
• D)400
• E)Any number between 640 and 656 is possible.

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Definitions:

Least Squares Regression

A statistical method for estimating the relationship between variables by minimizing the squares of the differences between observed and predicted values.

Relationship

A connection, association, or involvement between two or more variables or entities.

Standard Error

The standard deviation of the sampling distribution of a statistic, most commonly the mean.

Regression Slope

Indicates the steepness and direction of the linear relationship between two variables on a regression plot.