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 rectangular pen is fenced with 96 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 (no lid) with a square base must hold 62500 cm³. Use the least possible material, that is the smallest area of the base plus the four sides. Find the minimum surface area S.
An open box (no lid) with a square base must hold 62500 cm³. Use the least possible material, that is the smallest area of the base plus the four sides. Find the base side x.
A small firm sells its product at a fixed market price of €30 per unit. Producing q units costs C(q) = 800 + 20q + 0.02q² euros. Find the maximum profit P.
A small firm sells its product at a fixed market price of €80 per unit. Producing q units costs C(q) = 100 + 62q + 0.25q² euros. Find the maximum profit P.
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