A company finds that the rate at which the quantity of a product that consumers demand changes with 2000 respect to price is given by D'(x) = == where x is the price per unit, in dollars. Find the demand x² function if it is known that 502 units of the product are demanded by consumers when the price is $4.00 per unit. >

he quantity demanded each month of Russo Espresso Makers is 250 when the unit price is $136. The quantity demanded ach month is 1000 when the unit price is $106. The suppliers will market 750 espresso makers when the unit price is $80 er higher. At a unit price of $100, they are willing to market 2250 units. Both the supply and demand equations are known o be linear. (a) Find the demand equation. -1 -x + 146 25 p = (b) Find the supply equation. 1 x+ 70 p = 75* (c) Find the equilibrium quantity and the equilibrium price. |× units

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A TV channel has estimated the demand for its service to be givenby the following function: Q=9.83p-1.2A2.5Y1.6P0-1.4whereQ = monthly sales in unitsP = price of the service in $A = promotional expenditure in $’000Y = average income of the market in $’000P0 = price of ‘home movies’ in $ The current price of the TV channel is $60, promotional expenditure is$120,000, average income is $28,000, and the price of ‘homemovies’ is$45.Indicate whether the following statements are true or false, givingyour reasons and making the necessary corrections h. Current sales are over a million units a month. i. The demand curve for the channel is given by:Q=9.83p-1.2j. The channel’s sales are more affected by the price of ‘home movies’ than by the price of its own service.k. If the channel increases its price this will reduce its profit.