Questions: The linear profit function is P(x)=px-37x.

The linear profit function is P(x)=px-37x.
Transcript text: The linear profit function is $P(x)=p x-37 x$.
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Solution

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Solution Steps

To find the linear profit function \( P(x) \), we need to determine the profit per maintenance call. The profit function is generally given by the revenue function minus the cost function. Here, the revenue function is \( R(x) = 44x \) and the cost per call is given as \( 37x \). Therefore, the profit function can be expressed as the difference between these two functions.

Step 1: Define the Revenue and Cost Functions

The revenue function for \( x \) maintenance calls is given by: \[ R(x) = 44x \]

The cost function for \( x \) maintenance calls is given by: \[ C(x) = 37x \]

Step 2: Derive the Profit Function

The profit function \( P(x) \) is the difference between the revenue and the cost functions: \[ P(x) = R(x) - C(x) = 44x - 37x \]

Simplifying the expression, we get: \[ P(x) = 7x \]

Step 3: Calculate the Profit for 10 Maintenance Calls

Substitute \( x = 10 \) into the profit function: \[ P(10) = 7 \times 10 = 70 \]

Final Answer

The profit for 10 maintenance calls is \(\boxed{70}\).

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