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.
A farmer has 240 m of fencing to enclose a rectangular field along a straight river. No fence is needed along the river. Find the largest area A that can be enclosed.
An open box (no lid) with a square base must hold 32000 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 450 m² is fenced on all four sides. The side along the street, of length x, costs €40 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 = 80 − 0.25q euros per unit, and the cost is C(q) = 1000 + 30q euros. Find the maximum weekly profit P.
A theatre sells 1350 tickets per show at €12 each. Market research shows that every €1 increase in the ticket price means 50 fewer tickets sold (and every €1 decrease, 50 more). Find the maximum revenue R per show.
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