Suppose that the quantity supplied S and quantity demanded D of T-shirts at a concert are given by the following functions where \( p \) is the price. \[ \begin{array}{l} S(p)=-340+40 p \\ D(p)=1100-50 p \end{array} \] Ariswer parts (a) through (c). (a) Find the equilibrium price for the T -shirts at this concert. The equilibrium price is \( \$ 16 \) (Round to the nearest dollar as needed.) What is the equilibrium quantity? The equilibrium quantity is 300 T-shirts. (Type a whole number.) (b) Determine the prices for which quantity demanded is greater than quantity supplied. For the price \( \$ \) \( \square \) p \( \square \) \$ \( \square \) , the quantity demanded is greater than quantity supplied.

To solve the problem, we will follow the steps outlined: ### Part (a): Find the equilibrium price and quantity 1. **Set the supply function equal to the demand function** to find the equilibrium price: \[ S(p) = D(p) \] Substituting the given functions: \[ -340 + 40p = 1100 - 50p \] 2. **Combine like terms**: \[ 40p + 50p = 1100 + 340 \] \[ 90p = 1440 \] 3. **Solve for \( p \)**: \[ p = \frac{1440}{90} = 16 \] Thus, the equilibrium price is \( p = 16 \). 4. **Substitute \( p = 16 \) back into either the supply or demand function to find the equilibrium quantity**: Using the supply function: \[ S(16) = -340 + 40(16) = -340 + 640 = 300 \] So, the equilibrium quantity is 300 T-shirts. ### Part (b): Determine the prices for which quantity demanded is greater than quantity supplied 1. **Set up the inequality**: \[ D(p) > S(p) \] Substituting the functions: \[ 1100 - 50p > -340 + 40p \] 2. **Combine like terms**: \[ 1100 + 340 > 50p + 40p \] \[ 1440 > 90p \] 3. **Solve for \( p \)**: \[ p < \frac{1440}{90} = 16 \] Thus, the quantity demanded is greater than the quantity supplied when the price is less than \( 16 \). ### Final Answer for Part (b): For the price \( \$ \) \( \square \) p \( \square \) \$ \( 16 \), the quantity demanded is greater than quantity supplied. ### Summary: - (a) Equilibrium price: \( \$ 16 \), Equilibrium quantity: 300 T-shirts. - (b) For the price \( \$ \) \( p < 16 \) \( \), the quantity demanded is greater than quantity supplied.