Dynamic Calculus
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The bottom line
The revenue '\(R\)' received by a company is described in terms of the number of units '\(s\)' of an item that are sold. The marginal revenue '\(MR\)' is the derivative of the revenue function. For a particular company, the marginal revenue from the sale of a product is given by the equation \(MR = 4s + 13\). How do we calculate the revenue received?
[You can reset the applet at any time by clicking the 'circular arrows' icon in the top right corner]
- Given that \(MR = 4s + 13\), use the process of anti-differentiation to find the revenue function, \(R\). Confirm your answer by clicking the 'show anti-differentiation' checkbox.
- The primitive function \(R\) represents a family of curves, each member of which corresponds to a unique value of the constant, \(k\). Move the slider 'k' and observe other possible graphs of the revenue function.
- In the context of this problem, what is the only valid value of \(k\)? [Hint: What revenue would the company receive if zero units were sold?] Move the revenue function to its correct position by moving the slider k.
- How much revenue will the company receive from the sale of 50 units of the product? Check your answer by clicking the 'show revenue calculation' checkbox.
- What is the minimum number of units the company must sell in order to receive revenue in excess of $1000?