Calculus 3.3 Optimization problems full steps and full answer please.

Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A box is to be constructed from a sheet of cardboard that measure 24 cm x 24 cm. A square from each corner of the sheet will be cut and then the sides will be folded up to create the box. What is the greatest volume this box can be if it is constructed in this manner? a. 264.5 cm3 c. 1024 cm3 b. 759 cm3 d. 276.125 cm3 2. If a rectangle has a fixed area of A = xy, which value for x and y (in terms of A) will minimize the perimeter? a. x = NA, y= NA C. x = 3A, y = b. x = 24, y = 7 d. x= A, y= A 3. A rectangle is to be placed in the first quadrant, with one side on the x-axis and one side on the yaxis, so the rectangle lies below the parabola y+ 3x = 4. What is the maximum area of this rectangle? a C. WIN b. N d. 3 4. A certain poster requires 144 cm for the printed message and must have a 4-cm margin on each side. Determine the overall dimensions of the poster if the publisher wants to use the least amount of paper. a. 12 cm x 12 cm c. 12.3 cm x 12.3 cm b. 16 cm x 16 cm d. 12 cm x 16 cm 5. What are the dimensions of a rectangle with an area of 100 cm and the smallest possible perimeter? a. 5 am x 20 cm c. 10 cm x 10 cm b. 2 cm x 50 cm d. 4 cm x 25 cm