A rectangular pen is fenced with 48 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 240 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.
A rectangular plot of 400 m² is fenced on all four sides. The side along the street, of length x, costs €30 per metre; the other three sides cost €5 per metre. Find the length x of the street side that minimises the cost.
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 minimum surface area S.
A company sells q units per week. The price at which it can sell them is p = 160 − 2q euros per unit, and the cost is C(q) = 400 + 40q euros. Find the weekly output q that maximises profit.
A small firm sells its product at a fixed market price of €65 per unit. Producing q units costs C(q) = 27600 + 18q + 0.01q² euros. Find the output q that maximises profit.
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