HOMEWORK PROBLEM The management of the UNICO department store has decided to enclose an843ft 2 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$2 running foot, determine the dimensions of the enclosure that can be erected at minimum cost (Round your answers to one decimal place ) 2) A pencil cup with a capacity of80in 3 is to be constructed in the shape of a rectangular box with a square base and an open top If the material for the sides costs36 in 2 and the material for the base costs90 in 2 , what should the dimensions of the cup be to minimize the construction cost 3) A book designer has decided that the pages of a book should have 1 in margins at the top and bottom and1 2 in margins on the sides She further stipulated that each page should have an area of50in 2 (see the accompanying figure) Determine the page dimensions that will result in the maximum printed area on the page 4) For its beef stew, Betty Moore Company uses aluminum containers that have the form of right circular cylinders Find the radius and height of a container if it has a capacity of37in 3 and is constructed using the least amount of metal (Round your answers to two decimal places )

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HOMEWORK PROBLEM The management of the UNICO department store has decided to enclose an843ft 2 area outside the building for displaying potted plants and flowers.

HOMEWORK PROBLEM

The management of the UNICO department store has decided to enclose an843ft²area 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$2/running foot, determine the dimensions of the enclosure that can be erected at minimum cost. (Round your answers to one decimal place.)

2) A pencil cup with a capacity of80in.³is to be constructed in the shape of a rectangular box with a square base and an open top. If the material for the sides costs36/in.²and the material for the base costs90/in.², what should the dimensions of the cup be to minimize the construction cost?

3) A book designer has decided that the pages of a book should have 1-in. margins at the top and bottom and1/2-in.

margins on the sides. She further stipulated that each page should have an area of50in.²(see the accompanying figure). Determine the page dimensions that will result in the maximum printed area on the page.

4) For its beef stew, Betty Moore Company uses aluminum containers that have the form of right circular cylinders. Find the radius and height of a container if it has a capacity of37in.³and is constructed using the least amount of metal. (Round your answers to two decimal places.)