Question

Collection 2 Quadratic word problems (pick one of the following) Two rectangular lots are to be made from 400 ft. of fencing as seen to the right. Determine the dimensions that will maximize the area. The fuel economy (in miles per gallon) of a particular vehicle can be modeled by the function F(s) = 965 +9.1-.008s2 where s is the speed of the vehicle in miles per hour. What speed maximizes the fuel economy? What is the fuel economy if the vehicle is travelling at 35 mph? A company that makes and sells riding lawnmowers determines that the demand for lawnmowers is p(x) x + 1880 How many lawnmowers must be sold to maximize revenue and what price must be charged for the lawnmowers to maximize revenue? 1 10

Answer 1

82 e 96 S dimensions aft 1. Let each the foro rec of longles made from 400 ft. T fancing, ane andy ft. 27 2 (ary) - 400 Then 100 2-4 = maximize the total area howe 2xy -(424) 05 [city ) - (*-4)] € / 1 (nty)? where the equality n=7. holds when and when 2-Y Area Grill be maximum then from (1) => 20 = 408>) 2 = = 30 to rectangles dimensions of Readi 50 50 Do ft x 2000 fr. are 0.008x² 2. F(8) = 0.96 8 + 911 2 0.96s 9.1 oroo8 s s) 2 9i/ [ 7000 100 2 12 10 کہ 2 gol [ To = 70 9./ 2 + 0136 = 9.46 s 9.46 018 ["s) 2 (0-18)(016) +(0:4)3] 018 { Col S.4 0:622} --** Where equality holds when Orls=06 »s=6

ahon s=6 maximum .: F(A) will speed maximizes the fuel At 6 mile/hery economy. Cread.) 35 mph 18 when D. 35 If the vehicle is travelling at then the full economy is F(35) 9.476 - 08 ["0/135- 0:47' from us? 9:46 - 08 [35-0-67? 9:46 – 0.8 x (219) 2 9146- 0.8 x 8.41 2 9:46-6728 per gallon . 2.732 miles (Read>

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