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 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 length x that gives the largest total 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 minimum total cost C.
A rectangular plot of 200 m² is fenced on all four sides. The side along the street, of length x, costs €15 per metre; the other three sides cost €8 per metre. Find the length x of the street side that minimises the cost.
A small firm sells its product at a fixed market price of €75 per unit. Producing q units costs C(q) = 900 + 56q + 0.02q² euros. Find the maximum profit P.
A theatre sells 780 tickets per show at €25 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 ticket price p that maximises revenue.
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