Question

[3 marks] A rectangular box has its square bottom and three of its sides made of cardboard. The front and the square top are made of clear plastic. Plastic for the top and font costs $2 m- and cardboard costs $17m². If $3 is spent for each box, how many m- of plastic are used in the top of each box when the volume is maximized? Round your answer to two decimal places.

Answer 1

Giren: A rectangular box with say edge of square ke u и вых Area (A) of clear plastic = Square bottom. square bottom h solution: Area y Top + Area of Front Al x2 + xh Area (A2) of Cardboard Area of bottom & Area q 3 Sides. 2²+ sah. Az say Total Lost (c) for making the box cost (6) 2XA, 1. Az cost of plastic = $2/m2 Lost y Candboard 41 m² (i) 2Ait AL Each box was spent with $3 each boxi الم 2 A, A2 3 1 3 2 (x?tach) + (22+ 3xeh) 22² +22h + a²+ 3xch 3x² + 5xh 3 = 3 x² + sah :3 h - 3-30 5a Now Volume 4. box base Area x height v e².h x Каракцһе 2-3х- 5x 22 V 2 w 3-30 (5*) va 3 w 3 3 5 2 5 for volume masimum pur du di no Critical point.

dv d 2 3 . 3- 5 за 3 2х- а? са -(И 3 2. Put х the Area of to Тое -, ie т 5 2. Ахь 4 Top = ANS, (5) so Plastic used in Top of Box= 3 o, 133 2. OY