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 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 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 €20 per metre; the other three sides cost €8 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 base side x.
A small firm sells its product at a fixed market price of €40 per unit. Producing q units costs C(q) = 2300 + 10q + 0.02q² euros. Find the maximum profit P.
A theatre sells 360 tickets per show at €12 each. Market research shows that every €1 increase in the ticket price means 10 fewer tickets sold (and every €1 decrease, 10 more). Find the maximum revenue R per show.
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