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anonymous
 5 years ago
Let's construct a box whose base length is 3 times its base width and will have no lid. We only have 64 m2 of material to use. Determine the dimensions of the box that will give the largest volume.
___width?
___height?
___length?
What is the volume of the box?
ANY HELP ON HOW TO START THIS PLEASE??
anonymous
 5 years ago
Let's construct a box whose base length is 3 times its base width and will have no lid. We only have 64 m2 of material to use. Determine the dimensions of the box that will give the largest volume. ___width? ___height? ___length? What is the volume of the box? ANY HELP ON HOW TO START THIS PLEASE??

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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0we know that the surface area has to equal 64m^2 right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0our dimensions can be l,w,h were l = 3w

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0surface area = 3w(w) + 2(hw) + 2(3wh) = 64

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0volume of the box = 3w(w)h

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.064 = 3w^2 +2wh +6wh 64 = 3w^2 +8wh solve for "h" 64  3w^2 = 8wh 643w^2  = h 8w

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0use this "value" of h in the formula for the volume: V = 3w^2 [(643w^2)/8w]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0V = (192w^2  9w^4)/8w ; now simplify

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0V = (192x 9w^3)/8 find the derivative of this Volume function to determine critical numbers

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.08(19227w^2)  8(8) 19227w^2  solve for zero 8 192  27w^2 = 0 gonna be tricky for me without pencil and paper :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0got it.. 3(649w^2) = 0 649w^2 = 0 (8+3w)(83w) = 0 w = 3/8 or w = 3/8 since a negative width is meaningless; lets use w = 3/8

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0recall that l = 3w: l = 3(3/8) = 9/8

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0643w^2  = h 8w 64  3(3/8)^2  = h 8(3/8) 64  (27/64)  = h 3

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.04069/64  = h 3 4069/192 = h might need to reduce that....
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