A rectangular pen is fenced with 144 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.
A rectangular pen is fenced with 120 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 length x that gives the largest total area.
An open box (no lid) with a square base must hold 4000 cm³. Use the least possible material, that is the smallest area of the base plus the four sides. Find the height h.
A rectangular plot of 200 m² is fenced on all four sides. The side along the street, of length x, costs €25 per metre; the other three sides cost €8 per metre. Find the minimum total cost C.
A company sells q units per week. The price at which it can sell them is p = 180 − 0.25q euros per unit, and the cost is C(q) = 12800 + 20q euros. Find the price p that maximises profit.
A company sells q units per week. The price at which it can sell them is p = 150 − 0.2q euros per unit, and the cost is C(q) = 8300 + 35q euros. Find the maximum weekly profit P.
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