Let x = the width and the length of the base (a square). Based on the information given,
Surface Area = 2x2 + 4x(x+3) = 4x2 + 12x
= 6x2 + 12x >= 90
= 6x2 + 12x -90 >= 0
= x2 + 2x - 15 >= 0 Then (x+5)(x-3) >= 0
This leaves -5 & 3 as solutions and -5 is not a real world solution!
So, the base dimension is x = 3 and the Height = 3+3 = 6
Check the value of the Surface Area: 6(3)^2 + 12(3) = 90
Charles L.
Oh, I see, thanks for the help
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08/06/19
Charles L.
The only problem is that the solution is incorrect, when I input it into the system, it says incorrect.
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08/06/19
Mark J.
tutor
Charles, plot the graph and you will see that -5, & 3 are the correct points to make the surface area greater than or equal to 90. Also, the requirement that the base dimension be 3 units less that the height. I calculated the surface area assuming the box had a top. Perhaps they don't want a top on it. I originally thought that the answer would have to be 3+ but when 3 is substituted back into the surface area, you get 90 which is part of the requirement?? Check that .... if it has not top, the equation changes? Also, only the outside surface area was used and used in the calculation... normal practice! I also ran it in the EXCEL linear programming Solver and the answer came out as 3 for x? Check to see if the premises are correct. Thanks
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08/07/19
Charles L.
So what will end up being the overall solution?08/06/19