Question

A container manufacturer plans to make rectangular boxes whose bottom and top measure 2x by 4x. The container must contain 16 f? The top and the bottom will cost $2.80 per square foot, while the four sides will cost $4.30 per square foot What should the height of the container be so as to minimize cost? Round your answer to the nearest hundredth,

Answer 1

z For the rectangular box length = = 40 ft width 2xft height = hit (say) i. Volume = 41.20. h= 16 (given) 8x3h = 16 x h 22 h = 2 x2 Area of top & bottom in total (2x - 4x + 2x.4x) fth (82 +8+4) ft² z 16x² ft² :. Cost for it 16x2 x 2.80 dollar 44.8x² dollar Area of four sides = casa (22x2 + 2axh+4xxh +42xh ) It' = (22h + 2 2h+4x2+42h) ft² = 12h ft² - Cost for it - 12 24 x 4.30 dollar = 516 xh dollar : Total cost (e) = 44.8x²+516xh 44.812 +516x. 2 K² = 44.88²+ 101-2 2 der 44.8 x 22 - 103.2 x² = 0 x ² = 1032 = 11518 44 8X2 = 1.048 :. * (1.1518) = 1.821 ..ha 2 2² 4:0487 : Height of the container should be 1.821 ft. Note dre 23. dar = 448 X2 - 103*2 (-2)*-} = 89*6+ 20614 >o i dre da2x = 1048 89.6+ 206.4 (1.048) 3 in A minima exists here.