QUESTION 1

The supply function for oil is given (in dollars) by S(q), and the demand function is given (in dollars) by D(q). s(q) = q~ + 14q, D(q) =930 - 18q - qc. Find the consumers' surplus. The consumers' surplus is SD. (Type an integer or decimal rounded to the nearest hundredth as needed.) d. Find the producers' surplus. The producers' surplus is SD. (Me an integer or decimal rounded to the nearest hundredth as needed.) X A worker sketches the curves 5: = 53/; and y = E on a sheet of metal and cuts out the region between the curves to form a metal plate. Find the area of the plate. The area of the plate is (Type an integer or a simplied fraction.) Suppose a company wants to introduce a new machine that will produce a rate of annual savings (in dollars) given by the function S'(x), where x is the number of years of operation of the machine, while producing a rate of annual costs (in dollars) given by the function C'(x) l 2 .. 2 8 S{x)=216-x , C(x)=x +gx. a. For how many years will it be profitable to use this new machine? The number of profitable years is b. What are the net total savings during the first year of use of the machine? The net total savings during the first year of use of the machine is $ (Round to the nearest dollar as needed.) c. What are the net total savings over the entire period of use of the machine? The net total savings over the entire period of use of the machine is $ (Round to the nearest dollar as needed.)