Question

Due in 9 hours, 26 minutes. Due Sun 04/05/2020 11:59 pm Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Springfield and Shelbyville. There needs to be cable connecting Centerville to both towns. The idea is to save on the cost of cable by arranging the cable in a Y-shaped configuation Centerville is located at (9,0) in the ary-plane, Springfield is at (0,3), and Shelbyville is at (0 - 3). The cable runs from Centerville to some point (,0) on the r-axis where it splits into two branches going to Springfield and Shelbyville. Find the location (,0) that will minimize the amount of cable between the 3 towns and compute the amount of cable needed. Justify your answer. To solve this problem we need to minimize the following function of f(x) = Preview We find that f(a) has a critical number at Preview ) and find that To verify that f() has a minimum at this critical number we compute the second derivative S' its value at the critical number is Preview , a positive number Thus the minimum length of cable needed is Preview Get Help: Points possible: 4 This is attempt 1 of 3 Port this cuestion to con Submit W

Answer 1

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Solution: tel- c, s, i respectively represent the positions, lifcations a centre ville, Springfield and (0:3) Shelbyville and Peo) be a pornit to whick cable from a goes and -5 oC19,0) (0,3VY gets split into two parts going to go through ps and tou through Pv. U en clearly: Op=a, re=9, os=3 or 3. PCoC-of-9-2. shus: VA). Amount of cable used a cP+ PS + pv. flx) = (9-x) + 5x ² + 3² + 5x ² +3? F1x) = (2 842+9 + 9-x)] Aus, to f(x) has a critical number if: . f'(x)=0-> (F(11)=005, 01.12 172+ + 9-X) -0. -4309 2X= 4e279 2572+ 3 482=2279 y 3x2=93) 2?=3 x= 15 But the length: a = 1 is the critical number. Am. des None.of"(a) = (slay = 1) ga (79) At th: IMA) omon 7 flaj is MINIMIZES aé (x=88. | . MINIMUM lempthy Caste: 483)= 21879 +9-15 2 41379-3 = 9+3/3