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 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 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 minimum surface area S.
A rectangular plot of 1200 m² is fenced on all four sides. The side along the street, of length x, costs €30 per metre; the other three sides cost €10 per metre. Find the length x of the street side that minimises the cost.
A company sells q units per week. The price at which it can sell them is p = 70 − 0.5q euros per unit, and the cost is C(q) = 400 + 25q euros. Find the weekly output q that maximises profit.
A small firm sells its product at a fixed market price of €80 per unit. Producing q units costs C(q) = 100 + 58q + 0.25q² euros. Find the output q that maximises profit.
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