A rectangular pen is fenced with 144 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 length x that gives the largest total area.
A closed cylindrical can (with a top and a bottom) must hold 250 cm³. The metal used is proportional to the total surface area. Find the smallest possible surface area A.
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 theatre sells 440 tickets per show at €15 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 ticket price p that maximises revenue.
A company sells q units per week. The price at which it can sell them is p = 180 − 0.1q euros per unit, and the cost is C(q) = 2700 + 120q euros. Find the price p that maximises profit.
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