A Firm Produces Output at Two Plants That Are at Different

question 38

Essay

A firm produces output at two plants that are at different locations but are otherwise identical. The firm's cost function is C(q) = 5.3√q, where q is the quantity produced at the plant. To satisfy demand at the current market price, the firm needs to produce a total of 202,500 units of output. How should the firm divide production between the two plants in order to minimize the cost of production? Is it more profitable to produce all 202,500 units at one plant?

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Definitions:

Observed Z Value

The Z Score calculated based on sample data, representing the number of standard deviations a data point is from the mean.

Sample Mean

The average value of a sample set of numbers, calculated by summing all the observations and dividing by the number of observations in the sample.

Population Average

The sum of all the values in a population divided by the number of values, representing the central tendency of the population data.

Standard Error

The standard deviation of the sampling distribution of a statistic, often used in the context of estimating the population mean.