Find the market equilibrium point for the following demand and supply functions. Demand: \( p=-4 q+306 \) Supply: \( \quad p=6 q+3 \)

To find the market equilibrium point, we need to set the demand function equal to the supply function. The equilibrium occurs where the quantity demanded equals the quantity supplied. Given the demand function: \[ p = -4q + 306 \] and the supply function: \[ p = 6q + 3 \] We set the two equations equal to each other: \[ -4q + 306 = 6q + 3 \] Now, we will solve for \( q \). 1. Add \( 4q \) to both sides: \[ 306 = 10q + 3 \] 2. Subtract \( 3 \) from both sides: \[ 303 = 10q \] 3. Divide both sides by \( 10 \): \[ q = 30.3 \] Now that we have the equilibrium quantity \( q \), we can substitute it back into either the demand or supply function to find the equilibrium price \( p \). We'll use the supply function: \[ p = 6q + 3 \] Substituting \( q = 30.3 \): \[ p = 6(30.3) + 3 \] \[ p = 181.8 + 3 \] \[ p = 184.8 \] Thus, the market equilibrium point is: \[ (q, p) = (30.3, 184.8) \] In conclusion, the equilibrium quantity is \( 30.3 \) and the equilibrium price is \( 184.8 \).