A rectangular pen is fenced with 72 m of fencing and divided into two parts by one extra fence parallel to the sides of length x (three fences of length x and two of length y in total). Find the largest total area A that can be enclosed.
An open box is made from a rectangular sheet of cardboard 10 cm × 16 cm by cutting equal squares of side x from the four corners and folding up the sides. Find the largest possible volume V.
An open box (no lid) with a square base must hold 108000 cm³. Use the least possible material, that is the smallest area of the base plus the four sides. Find the height h.
An open box (no lid) with a square base must hold 13500 cm³. Use the least possible material, that is the smallest area of the base plus the four sides. Find the height h.
A small firm sells its product at a fixed market price of €75 per unit. Producing q units costs C(q) = 100 + 50q + 0.5q² euros. Find the maximum profit P.
A small firm sells its product at a fixed market price of €35 per unit. Producing q units costs C(q) = 100 + 14q + 0.25q² euros. Find the maximum profit P.
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