Cubic Foot
November 12th, 2009
A certain magical substance used to make magical solid spheres cost per cubic foot. The power of amendment?
A one magical substance that is used to make magical cost per cubic foot solid spheres. The magical power of a sphere depends on its surface, and a magic sphere can be sold per square foot. If you are doing as a sphere, what size should do to maximize your benefits by area
What You Need do is work for the benefit base "a". Its cost is proportional to the volume of a sphere: V / 3 * pi * r ^ 3 = 4 C = x / 3 * 4 * pi * r ^ 3 (where X is the cost per unit volume) = qr C ^ 3 (q = x * 4 / 3 * pi) Your payment will be linked to the surface. 4 * pi * r ^ 2 = PA y = 4 * pi * r * r * ^ 2 = P s ^ 2 (y = s * 4 * pi) Therefore, every area that PC Profit = qr 3 ^ – ^ sr 2 Now take the derivative with DProf r / dr = ^ 2-2 sr 3qr Maxima / Minima will be when the DProf / dr = 0 0 r = (2QR – 2) Thus either r = 0 or = s / t (for sure it is a maximum, not minimum, but I am sure that is a maximum) s = r / q = (4 * y * pi) / (xf 4 / 3 * pi) r = 3 S / X (simplification) (where X and Y are the costs per unit of volume and surface, respectively)
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