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Do Homework-Gabrielle Blanchard-Google Chrome Secure l https://www.mathxl.com/Student/PlayerHomework.aspx?homeworkld-469629879&questio..; Math 2103 20121 2018S Homework: 2.5 Maximum & Minimum Problems Score: 0.25 of 1 pt Save 6of2007 complete) HW Score: 3879%, 11.25. & Gen Interest 2.5.17 Assigned Media | , Question Help * Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 17 in, by 10 in. by cutting congruent squares from the corners and folding up the sides. Then find the volume The dimensions of box of maximum volume are Round to the nearest hundredth as needed Use a comma to separate answers as needed) Enter your answer in the answer box and then click Check Answer part emaining 10:19 PM

Explanation / Answer

Lets say, the side of square cut = x inches

So the length of the rectangular box= (17 - 2x)

and width = (10 - 2x)

height = x

So, the volume V = (17-2x)*(10-2x)*x

dV/dx= (17 - 2x)(10-4x) - 2x(10-2x)

put dv/dx =0

(17 - 2x)(10-4x) - 2x(10-2x)

On simplifying the above we get the following quadratic equation:

12x2-108x+170=0

Solving the quadratic equation we get feasible value of x:

x= 6.966 inches and 2.0335 inches

at x = 2.0335 inches f''(x) is less than zero.

So max volume occurs at x = 2.0335 inches

length = 17 - 2*2.0335 = 12.9330 inches

widht = 10 - 2*2.0335 = 5.9330 inches

height = 2.0335 inches

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