Questions: The total profit (in dollars) from the sale of (x) charcoal grills is [ P(x)=60 x-0.9 x^2-285 ]

Transcript text: The total profit (in dollars) from the sale of $x$ charcoal grills is \[ P(x)=60 x-0.9 x^{2}-285 \]

Solution

Solution Steps

To solve the problem of finding the total profit $ P(x) $ from the sale of $ x $ charcoal grills, we need to evaluate the given profit function $ P(x) = 60x - 0.9x^2 - 285 $. We can use Python to compute the profit for any given value of $ x $.

Step 1: Define the Profit Function

The total profit $ P(x) $ from the sale of $ x $ charcoal grills is given by the function: \[ P(x) = 60x - 0.9x^2 - 285 \]

Step 2: Calculate Profit for $ x = 10 $

To find the total profit when $ x = 10 $, we substitute $ 10 $ into the profit function: \[ P(10) = 60(10) - 0.9(10)^2 - 285 \] Calculating each term: \[ P(10) = 600 - 0.9(100) - 285 \] \[ P(10) = 600 - 90 - 285 \] \[ P(10) = 600 - 375 = 225 \]