Question

Based upon market research, the Hawthorne Company has determined that consumers are willing to purchase 133 units of their portable media player each week when the price is set at $46.20 per unit. At a unit price of $11.80, consumers are willing to buy 305 units per week. (a) Determine the weekly demand equation for this product, assuming price, p, and quantity, x, are linearly related. p (b) Determine the weekly revenue function. R(x) (c) Determine the number of units consumers will demand weekly when the price is $30.40 per portable media player. units (d) Determine the number of units consumers will demand weekly when the revenue is maximized. units (e) Determine the price of each unit when the revenue is maximized dollars -1.74 points TanFin9 1.4.028. 12. My Notes Ask Your Teacher The quantity demanded each month of Russo Espresso Makers is 250 when the unit price is $136. The quantity demanded each month is 1000 when the unit price is $106. The suppliers will market 750 espresso makers when the unit price is $68 or higher. At a unit price of $88, they are willing to market 2250 units. Both the supply and demand equations are known to be linear. (a) Find the demand equation. p= (b) Find the supply equation p (c) Find the equilibrium quantity and the equilibrium price. units Need Help? Watch It Talk to a Tutor

Answer 1

Two set of values Gf Pouice amd demand Given nantity of demand /week PE Ruantity of Pice /unit. Let (, P) = (133, 46. 29 and (221 Po) = (305, 11 80) As the 0, demand eqnation passing thorough two poin ts is demand function is 1inear eanation velue P-P (Plug in the Pi-P 21-K2 P-イ620 46 20-11.80 2-133 133-305 X-133 P-46.20 - 172 34 40 P-46 20 24.40 N-133 -172 7P=46.20-0.2(0133) 46.20-0122+ 26 50 Weekly demand eanation ラP -0.2 n + 72' 80 Revenue = Price x auantihy Demanded R=P, 2 (-0 2% t 72 80) 7Weekly Revenue function. Ra 0'2 x2 t 72 80 x in demand eanalion get Plug in P- $30.40 we 30 40=-0'2X +72'80 to.2 = 72 80-30.40 =42' 4 n 42.40/0.2 212 units weekly demand d'R Revenue wil be maximized whan 0 and R=-0272 80 x)= O -0.2(27) + 72.80= 0 Here 72-80 4 182 = Again d ( 042+72 80) = 0.4o Units Revenue maximized at X 182 Plug in e= 182 in demand eanatien we get, e dollars P= -0.2182)+72 80|36