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 rectangular pen is fenced with 120 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 closed cylindrical can (with a top and a bottom) must hold 400 cm³. The metal used is proportional to the total surface area. Find the height h of the can that uses the least material.
A rectangular plot of 600 m² is fenced on all four sides. The side along the street, of length x, costs €25 per metre; the other three sides cost €8 per metre. Find the length x of the street side that minimises the cost.
A company sells q units per week. The price at which it can sell them is p = 140 − 0.2q euros per unit, and the cost is C(q) = 7800 + 15q euros. Find the price p that maximises profit.
A theatre sells 1350 tickets per show at €15 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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