The problem states that a company will produce 20 units for a price of $31 and 40 units for a price of $32. We are asked to find the linear supply equation that relates the price $p$ to the quantity $q$. We have two points: $(q_1, p_1) = (20, 31)$ and $(q_2, p_2) = (40, 32)$.

1. Problem Description

The problem states that a company will produce 20 units for a price of $31 and 40 units for a price of$

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2. We are asked to find the linear supply equation that relates the price $p$ to the quantity $q$. We have two points: $(q_1, p_1) = (20, 31)$ and $(q_2, p_2) = (40, 32)$.

2. Solution Steps

Since the supply equation is linear, it can be expressed in the form $p = mq + b$, where $m$ is the slope and $b$ is the y-intercept.

First, we find the slope $m$:

$m = \frac{p_2 - p_1}{q_2 - q_1}$

$m = \frac{32 - 31}{40 - 20} = \frac{1}{20}$

Now, we have $p = \frac{1}{20}q + b$. We can use either point to solve for $b$. Let's use $(20, 31)$:

$31 = \frac{1}{20}(20) + b$

$31 = 1 + b$

$b = 30$

Thus, the linear equation is $p = \frac{1}{20}q + 30$.

3. Final Answer

The linear supply equation is $p = \frac{1}{20}q + 30$. So the answer is (c).