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 largest total area A that can be enclosed.
A farmer has 320 m of fencing to enclose a rectangular field along a straight river. No fence is needed along the river. Find the length x of each side perpendicular to the river for the largest area.
A rectangular plot of 1200 m² is fenced on all four sides. The side along the street, of length x, costs €25 per metre; the other three sides cost €10 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 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 theatre sells 820 tickets per show at €12 each. Market research shows that every €1 increase in the ticket price means 20 fewer tickets sold (and every €1 decrease, 20 more). Find the maximum revenue R per show.
A theatre sells 1450 tickets per show at €20 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 ticket price p that maximises revenue.
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