Show all work, thanks. ### Physics Club Sweatshirt Sales AnalysisThe Physics Club at Foothill College sells Physics Show sweatshirts at the yearly Physics Show event. A quadratic regression model based on previous sales reveals the following demand equation for the sweatshirts:\[ q = -p^2 + 33p + 9 \]\[ 18 \leq p \leq 28 \]Where:- $ q $ is the quantity of sweatshirts demanded- $ p $ is the price of the sweatshirtsAnalyzing this model involves answering the following questions:#### A) Determine the Price Elasticity of Demand (E) when the Price is set at $20. SHOW WORK.To determine the price elasticity of demand (E), we use the formula:\[ E = \left(\frac{dQ}{dp}\right)\left(\frac{p}{Q}\right) \]1. Calculate $ \frac{dQ}{dp} $:\[ q = -p^2 + 33p + 9 \]\[ \frac{dq}{dp} = -2p + 33 \]2. Substitute $ p = 20 $ into $ q $:\[ q = -(20)^2 + 33(20) + 9 \]\[ q = -400 + 660 + 9 \]\[ q = 269 \]3. Substitute $ p = 20 $ into $ \frac{dq}{dp} $:\[ \frac{dq}{dp} = -2(20) + 33 \]\[ \frac{dq}{dp} = -40 + 33 \]\[ \frac{dq}{dp} = -7 \]4. Calculate E:\[ E = \left(\frac{dQ}{dp}\right)\left(\frac{p}{Q}\right) \]\[ E = (-7)\left(\frac{20}{269}\right) \]\[ E \approx -0.52 \]#### B) Is demand elastic or inelastic at a price of $20? What will happen to revenue if we raise prices? Explain.Given $ |E| \approx 0.52 $ (which is less than 1), the demand is inelastic.**Explanation:**- If the price increases, the percentage decrease in quantity demanded will be smaller than the percentage increase in price.- Hence, raising prices will increase total revenue

The Physics Club at Foothill College sells Physics Show sweatshirts at the yearly Physics Show event. A quadratic regression model based on previous sales reveals the following demand equation for the sweatshirts: q = -p² +33p+9; 18≤p ≤28 A) Determine the price elasticity of demand E when the price is set at $20. SHOW WORK. B) Is demand elastic or inelastic at a price of $20? What will happen to revenue if we raise prices? Explain. C) At what price should sweatshirts be sold to maximize revenue? SHOW WORK. D) How many sweatshirts would be demanded if they were sold at the price that maximizes weekly revenue? SHOW WORK. E) What is the maximum revenue? SHOW WORK.