Question

The management of the UNICO department store has decided to enclose an 820 ft2 area outside the building for displaying potted plants and flowers. One side will be formed by the external wall of the store, two sides will be constructed of pine boards, and the fourth side will be made of galvanized steel fencing. If the pine board fencing costs $7/running foot and the steel fencing costs $3/running foot, determine the dimensions of the enclosure that can be erected at minimum cost. (Round your answers to one decimal place.) Video Help_Go to the 3:33 minute mark of video to see example. wood side 40 steel side 20 ft STORE Wood Steel Wood Viewing Saved Work Revert to Last Response

Answer 1

het n be the Land of the wooden side and or y be the dimension of the steel side. Criven Area = 820 ft 2 ny - 820 ..y 8200 Cost function - In + 3y + tn = 14m + 3y _ =14 +3 320 CCx) = Mm f 2460 2 for maxima minima d' x)=0 c'(x2= 14 - 2460 20 14 2460 > n2 = 2460 a 175.71428 ...no 13:2557 13.3 ft c"(x) = 6 - 2460 (-2) 2 - 1 = 2460x2 C (x = 13.3) = 2460x220 (13. 33 Here the cost will be minimum at x = 13.3ft. - .. y = 820 m = 820 = 61.654 133Ñ 61,714. • Wooden steel side side, x = 13.3ft y = 617 ft