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# Find the Marginal Revenue and Marginal Cost

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C(x)=5x+240 and P(x)=.3x+500
Find:
1. R(x)
2. the marginal revenue and marginal cost
3. an equation for x where marginal revenue and cost are equal

##### Solution Summary

Detailed steps on Manipulating Cost, Profit and Revenue Equations to find the Marginal Revenue and Marginal Cost as well as an overview of the key terms and their meaning.

##### Solution Preview

Student,

1. To calculate revenue, R(x) it is good to remember the relationship between the Profit, Revenue and Cost functions:
P(x) = R(x) - C(x)
That is, profit P(x) is what is left over after subtracting cost from revenue, which makes sense. This equation can be rewritten to solve for any one of the three, given the other two, in this case:
P(x) + C(x) = R(x)
(.3x+500) + (5x+240) = R(x)
5.3x+740= R(x)

2. The marginal revenue and marginal cost, ...

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