Question 1

The tables to the right give price-demand and price-supply Price-Demand Price-Supply data for the sale of soybeans at a grain market, where x is the number of bushels of soybeans (in thousands of X P = D(x) X p = S(x) bushels) and p is the price per bushel (in dollars). Use 6.63 0 6.40 quadratic regression to model the price-demand data and 10 linear regression to model the price-supply data. Complete 10 6.55 6.47 parts (A) and (B) below. 20 6.47 20 6.52 30 6.44 30 6.58 40 6.41 40 6.62 (A) Find the equilibrium quantity and equilibrium price The equilibrium quantity is thousand bushels (Round to three decimal places as needed.) The equilibrium price is $ per bushel. (Round to the nearest cent as needed.) (B) Use a numerical integration routine to find the consumers' surplus and producers' surplus at the equilibrium price level. The consumers' surplus is $ (Round to the nearest dollar as needed.) The producers' surplus is $ (Round to the nearest dollar as needed.)Find the consumers' surplus and the producers' surplus at the equilibrium price level for the given price-demand and price-supply equations. Include a graph that identifies the consumers' surplus and the producers' surplus. p = D(x) =80e-0-001x. ; p = S(X) =20 + 0.0001x2 The consumers' surplus is approximately $ (Round to the nearest dollar as needed.) The producers' surplus is approximately $ (Round to the nearest dollar as needed.) The graph of D(x) = 80e" is shown as a solid curve and the graph of S(x) = 20 + 0.0001x- is shown as a dotted curve. Choose the correct graph below. O A. O B O c. OD. 100- 100- AY 100- AY CS 1000 1000 1000 1000The number of voters (in thousands) in a certain city is given by N(t) =17 + 8t - 7te- 0.1t where t is time in years. Find the average number of voters during the period from t = 0 to t = 7. The average number of voters during the period from t = 0 to t = 7 is approximately (Round to the nearest whole number as needed.)Find the consumers' surplus (to the nearest dollar) at a price level of p = $2.088 for the price-demand equation p = D(x) = 9 - In (x + 6) Use x computed to the nearest higher unit. CS = $ (Simplify your answer. Round to the nearest dollar as needed.)Find the derivative of f(x) and the indefinite integral of g(x). f(x) = 3X; g(X) = X 5 f'(x) - g(x) dx =