The problem provides the supply and demand equations for a product: Supply: $p = 8q + 2$ Demand: $p = -2q + 32$ We need to find the equilibrium price.

1. Problem Description

The problem provides the supply and demand equations for a product:

Supply: $p = 8q + 2$

Demand: $p = -2q + 32$

We need to find the equilibrium price.

2. Solution Steps

The equilibrium price occurs when supply equals demand. Therefore, we set the two equations equal to each other and solve for $q$.

$8q + 2 = -2q + 32$

$8q + 2q = 32 - 2$

$10q = 30$

$q = \frac{30}{10}$

$q = 3$

Now that we have the equilibrium quantity, we can plug it back into either the supply or demand equation to find the equilibrium price. Let's use the supply equation:

$p = 8q + 2$

$p = 8(3) + 2$

$p = 24 + 2$

$p = 26$

Alternatively, using the demand equation:

$p = -2q + 32$

$p = -2(3) + 32$

$p = -6 + 32$

$p = 26$

3. Final Answer

The equilibrium price is $p = 26$.

The answer is (b).