## Example

The inverse supply for bananas is `P = 1 + 2 Q_s`.

If a banana is sold for $5, producers will produce `Q_s = \frac{5 - 1}{2} = 2`.

The Producer Surplus is `\text{PS} = \frac{\left( 5 - 1 \right) \times 2}{2} = \frac{4 \times 2}{2} = $4`.

### Question

The supply for bananas is `Q_S = \frac{P - 114}{57}`.

What is the Producer Surplus when the price is $798?

### Step 1: Quantity Supplied

At price $798, the quantity demanded is `Q_S = \frac{P - 114}{57} = \frac{798 - 114}{57} = 12`.

### Step 2: Inverse Supply

$$ \begin{align*} Q_S &= \frac{P - 114}{57} \\ 57 Q_S &= P - 114 \\ 114 + 57 Q_S &= P \end{align*} $$So the inverse supply curve follows the equation `P = 114 + 57 Q_S`.

### Step 3: Draw the graph

### Step 4: Calculate the Producer Surplus

`\text{PS} = \frac{(798 - 114) \times 12}{2} = 4104.0`