dH/dt = ∂H/∂x dx/dt + ∂H/∂y dy/dt
∂H/∂x = -13/(2√x)
∂H/∂y = 0.3√(0.1y+20)
dx/dt = 300
dy/dt = 10/√y
So, plug and chug, with t=2
A car dealer determines that if gasoline-electric hybrid automobiles are sold for x dollars apiece and the price of gasoline is y cents per gallon, then approximately H hybrid cars will be sold each year, where
H(x,y)=6000−13x^(1/2)+2(0.1y+20)^(3/2).
She estimates that t years from now, the hybrid cars will be selling for 40000+300t dollars apiece and that gasoline will cost 300+20t^(1/2) cents per gallon. At what rate will the annual demand for hybrid cars be changing with respect to time 2 years from now?
I have no clue how to even begin this problem.
2 answers
DEMAND FOR HYBRID CARS A car dealer determines that if gasoline-electric hybrid automobiles are sold for x dollars apiece and the price of gasoline is y cents per gallon, then approximately H hybrid cars will be sold each year, where H(x, y) = 3,500 – 19x/2 + 6(0.1y + 16)³/² She estimates that i years from now, the hybrid cars will be selling for x(1) = 35,050 + 350/ dollars apiece and that gasoline will cost 76. y(1) = 300 + 10(31)/2 cents per gallon. At what rate will the annual demand for hybrid cars be changing with respect to time 3 years from now? Will it be increasing or decreasing?
1 answer