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Do Homework - Ahmed Alaraimi - Google Chrome https://www.mathxl.com/Student/P aspx?homework ld = 381 2062 64&questionld-9;&flushed-true;&cld-4035701; &centerwin;=yes Math 273, fall 2016 Ahmed Alaraimi | 10/9/16 10:15 PM Homework: MML 12(12.8) Save Score: 0 of 1 pt 10 of 10 (10 complete) HW Score: 65%, 65 of 10 pts Question Help 12.8.60 A box is to be made where the material for the sides and the lid cost $0.20 per square foot and the cost for the bottom is S0.65 per square foot. Find the dimensions of a box with volume 20 cubic feet that has minimum cost. The box with volume 20 cubic feet that has minimum cost has lengt! ft wid ft, and height. ft. Round to four decimal places as needed) Enter your answer in the edit Tields and then click Check Answer Clear A Check Answer 1.11149 ENG 10:15PM ENG 10/9/2016 i l

Explanation / Answer

V = lwh = x x h = x2h  = 20

The bottom is just a square, so the area of bottom is x2 and hence cost for making bottom is 0.65x2

Similarly cost for making top is 0.25x2 and that of sides is 4(0.25xh)

Hence total cost for making box = 0.65x2 + 0.25x2 + xh = 0.90x2 + xh = C

Now we have xh = 20/x

So we get 0.90x2 + 20/x = C

Take derivative both sides with respect to x:

1.8x -20/x2 = dC/dx = 0

=> 1.8x = 20/x2

x3 = 20/1.8 = 11.11

=> x = 2.23

h = 20/(2.23)2 = 4.02

Length = 2.23 ft

Width = 2.23 ft

Height = 4.02 ft

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