# Canvas Beach Help with a calculus problem please!?

There is a problem in my task of calculation do not know how and really appreciate some help! "A haven for beach canvas AHS two square sides, a rectangular back and a rectangular lid. Suppose that 96 square meters of cloth to be used. Find size of the dwelling for which the volume is maximized. "I realize that people do not usually do that on other tasks for them, but if someone at least point the right direction or tell me what you really appreciate it.

Let x be the length and width and being. Volume and height = x ^ 2 area = 2xy 2 and ^ 2 = 96 2xy = 96-2y ^ 2 = x (96-2y ^ 2) Volume / 2a x = 48 / volume and y = (48/yy) y ^ 2 = 48y-y ^ 3 V = 48y-y ^ differentiate with respect to 3 and dV / dy = 48-3y ^ 2 = 0 3y ^ 2 = 48 and y = 2-16 ^ 4 — Height and width x = 48 / y – y = 48 / 4 – 4 = 8 – length dimensions are length of 8, 4 wide , height 4 d 2V/dy ^ ^ 2 =- 6y = -6 (4) =- 24 <0, thus maximizing V.

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