Given:
p + 2q = 20
p - q = 2
After solving the system of equations, we have:
p = 8
q = 6
Let's find the Consumer surplus (CS) and Producer surplus(PS).
To find the Consumer Surplus(CS), apply the formula:

Where;
Demand equation, dq: p + 2q = 20
p = 20 - 2q
p = 8
q = 6
Now, we have:
![\begin{gathered} [\int_0^6(20-2q)dq]-8*6 \\ \\ (20*6-20*0-2((6^2)/(2)-(0^2)/(2)))-48 \\ \\ (120-2(18))-48 \\ \\ 84-48 \\ \\ =36 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/biszx3sc3e0zkhsj0e3pvzhkfg6efkr8om.png)
Therefore, the Consumer Surplus is $36.
• Producer surplus:
To find the producer surplus, apply the formula:

Where:
Supply equation, qs: p - q = 2
Rewrite for p:
p = q + 2
Thus, we have:

Therefore, the Producer Surplus is $18.
ANSWER:
CS = $36
PS = $18