The management of the unico department store has decided to enclose an 833 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 $6/running foot and the steel fencing costs $2/running foot, determine the dimensions of the enclosure that can be erected at minimum cost. (round your answers to one decimal place.)

Question

Mathematics

Russell

31 March, 00:22

The management of the unico department store has decided to enclose an 833 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 $6/running foot and the steel fencing costs $2/running foot, determine the dimensions of the enclosure that can be erected at minimum cost. (round your answers to one decimal place.)

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Leila Casey · Answer 1

The dimensions would be 28.9 for the steel length and 28.8 for the pine boards, for a total cost of $403.40.

To maximize area and minimize perimeter, you want a figure that is as close to equilateral as you can get. Therefore we take the square root of our area:

√833 = 28.9.

Dividing 833/28.9 we get 28.8.

We want to use the shorter side, 28.8, for the pine boards, as they cost more. 28.8*2*6 = 345.60.

The cost of the steel side is given by 28.9*2 = 57.80.

Together it costs 345.60+57.80 = 403.40.