A rectangular pen is fenced with 360 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 largest total area A that can be enclosed.
A closed cylindrical can (with a top and a bottom) must hold 355 cm³. The metal used is proportional to the total surface area. Find the smallest possible surface area A.
A closed cylindrical can (with a top and a bottom) must hold 750 cm³. The metal used is proportional to the total surface area. Find the height h of the can that uses the least material.
A company sells q units per week. The price at which it can sell them is p = 80 − 0.1q euros per unit, and the cost is C(q) = 2400 + 40q euros. Find the price p that maximises profit.
A small firm sells its product at a fixed market price of €80 per unit. Producing q units costs C(q) = 1300 + 34q + 0.2q² euros. Find the maximum profit P.
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