6. Solve the following optimization problems. Be sure to identify the constraint equation and themaximizing/minimizing function, determine the domain of the optimizing function, check the second derivative foroptimum value, and write the answer in complete sentence including appropriate unitsa) If 1200cm? of metal is available to make a box with square base and open top, find the dimensions of the boxwith largest possible volume. Determine the maximum volume.b) A printed page is to have 1 in. margin on all sides. The page should contain 80 sq inches of type. What dimensionsof the page will minimize the area of the page while still meeting the other requirements?c) A running circuit is to be constructed in the shape of a rectangle with two semicircles attached at the east and westends of the path (see figure). A picnic area will be set in the center of the circuit. If we want the total length of the circuitto be 2,000m (2Km), what will be the dimensions (r and I) that make the picnic area maximum? Give you answer inmeters.

Name: 6. Solve the following optimization problems. Be sure to identify the
Uploaded: 2024-03-20T07:07:26.000Z
Channel: Bartleby
Description: 6. Solve the following optimization problems. Be sure to identify the constraint equation and themaximizing/minimizing function, determine the domain of the optimizing function, check the second derivative foroptimum value, and write the answer in c