Question

A dumpster is being manufactored with volume of 350 cubic feet. It costs $1.25 for the bottom per square feet and $0.75 for the sides per square feet.

1. what dimensions will minimize the cost?

2. what is the minimum cost? $______

Answer 1

Given Volume 350 ft Cost of side 2 $0.75 ift? bottom: $1025 Ift² and m, breadth Let the lingen, dumpster be x, y, z height of the respectively (volume & length 350 x bread to height) ny za Area bottom a 2 2uzt of Lost of bottom sy Area of rides 7 + 2y z 1. 25ry sides - 0.75 (242 +242) 1057 (nty) Cost of Total lost Lost a 1.25 1.25 mg + 1.52(way) know syz 2350 ) Z 2350 ny Da 2 z 350 in the total Cost to reduce put ny number of variables, Total lost + 1.5x350 x (nry) 1.25 ny my

Let the total cost minimize 525 525 -1 be flany). We need to finy fm.yle 1o2sny te (ny) - 1.asy y² The extreme values occur where for aty - o y 525 10 25x- 525 fylmy). M - 525 and 1.25x = 525 2. 1.asy - y = 120 y 420 in put y. 212 1-25n = 525 >> 1.25n = 525n4 (420)2 (420)2 x4 2 x = (420) x1,25 525 23 - 420 2) r = 7.4889 420 724889. =) Y = (1-1889) entreme Value at Thus, there is (7.4889, 7.4889). Now Minima hel's check if ih

1050 from boy) logo tyg (any). los 2 1.25 fox fyy fry 2 D (7.4889, 7.4889). 1050 1050 (1.25) (4.4889) (7.4889)3 2. *(2.5) (1-25) D7 o Hence flmy has muuma at (7.4889, 7.4889) Z= 350 350 z x 6.2409 (1-4889) breadth and thus the length height of 4.4889 ft, 74889 ft the dumpster 6-2407 ft respectively are and