Question

Find the profit function P(x) where x represents the number of cookies sold

Hint: Profit = Total Revenue - Total Cost
Total Revenue = Price per unit x quantity sold
Total Cost = Total variable cost + fixed cost​

Answer 1

The profit function P(x) for the number of cookies sold x is
`\( P(x) = p \cdot x - VC - FC \)`, where p is the price per unit, VC is the total variable cost, and FC is the fixed cost.

The profit function P(x) is determined by subtracting the total cost from the total revenue:

`\[ P(x) = \text{Total Revenue} - \text{Total Cost} \]`

The total revenue TR is given by the product of the price per unit p and the quantity sold x:

`TR = p \cdot x`

The total cost TC is the sum of the total variable cost VC and the fixed cost FC:

TC = VC + FC

Now, substitute these into the profit function:

`\[ P(x) = TR - TC \]\[ P(x) = (p \cdot x) - (VC + FC) \]`

So, the profit function is
`\( P(x) = p \cdot x - VC - FC \)`.