Find the most economical dimensions of a closed rectangular box of volume
Answers
Explanation:
It would make more sense if you would specify what x, y, and z represent at the start. I assume you mean that x and y are "length" and "width" and z is "height". In any case, yes, the volume satifies xyz= 8 and the "cost" is 10xy+ 4xz+ 10yz. You can write each of your erquations as 10 y + 4 z = − λ y z 10y+4z=−λyz 10 x + 10 z = − λ x z 10x+10z=−λxz and 4 x + 10 z = − λ x y 4x+10z=−λxy Since the value of λ λ is not important to the solution, I like to eliminate it first by dividing one equation by another: If you divide the first equation by the second you get 5 y + 2 z 5 x + 5 z = y x 5y+2z5x+5z=yx and if you divide the first equation by the third you get 5 x + 2 z 2 x + 5 z = z x 5x+2z2x+5z=zx Those, together with x y z = 8 xyz=8 give you three equations to solve for x, y, and z.