The following tables give price–demand and price–supply data for the sale of soybeans at a grain market, where x is the number of bushels of soybeans (in thousands of bushels) and p is the price per bushel (in dollars):

Use quadratic regression to model the price–demand data and linear regression to model the price–supply data.

(A) Find the equilibrium quantity (to three decimal places) and equilibrium price (to the nearest cent).

(B) Use a numerical integration routine to find the consumers’ surplus and producers’ surplus at the equilibrium price level.

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Tables for 85-86 Price-Demand Price-Supply p = D(x) p = S(x) 6.70 6.43 10 6.59 10 6.45 20 6.52 20 6.48 30 6.47 30 6.53 40 6.45 40 6.62