Bicycles. A local company that manufactures and sells bikes has found that its monthly revenue (in dollars) is given by R(x,y) = 2 X2 2.5 y2 2 xy + 400 x + 320 y where X is the number of mountain bikes and y is the number of city bikes that it sells each month. (a) The critical point of R(x,y) is (0,0) (80,15) (85,30) (70,50) There is no critical point (30,85) (50,70) (15,80) (b) Let D(X,y)=RXX(X,y)Ryy(X,y)ny2(x,y). Suppose that a is the number of mountain bikes and b is the number of city bikes that should be sold each month to ensure a maximum monthly revenue. Which of the following statements is true? D(a,b) = 0 D(a,b) o D(a,b) o and RXX(a,b) 0 and RXX(a,b) > 0 Revenue. Suppose the graph of the revenue R(x) and cost C(X) are shown below where R(X) = X2-2.5x+2 and C(x) = x2 + 2 y 4 ax) 3 Run 1 The profit, or the area enclosed between the two curves is Note: Round to 4 digits after the decimalr point, if rounding is required 10.6667 -10.6667 -0.651 0.651 6.9375 0 -6.9375 none of the other answers Suppose the price of [and in a city is given by the function 1 2 2 P(x,y) = 495 10(X 3 15(y 1) where P(x,y) is the price of land at the point (x,y) in dollars per square metre and x and y are measured in kilometres. At what point within the city is the price of land highest? (-r-) (0,0) None of the other answers (2.2) () ($1) (1,1) (1%) A cell phone company estimates that 1' months after releasing a new model of their phones, the total number of units sold (in millions) will be given by N(t) = 10(1 s t s 12. (a) About how many units will be sold 2 months after the release of the new model? 5.1 thousand 5.1 billion 26.3 billion None of the other options 26.3 thousand (b) How fast will the new model be selling 2 months after its release? 1.6 million/month 2.2 million/month 12.0 million/month 4.4 million/month 6.0 million/month