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.
An open box is made from a rectangular sheet of cardboard 30 cm × 48 cm by cutting equal squares of side x from the four corners and folding up the sides. Find the largest possible volume V.
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 closed cylindrical can (with a top and a bottom) must hold 330 cm³. The metal used is proportional to the total surface area. Find the radius r that uses the least material.
A theatre sells 725 tickets per show at €15 each. Market research shows that every €1 increase in the ticket price means 25 fewer tickets sold (and every €1 decrease, 25 more). Find the ticket price p that maximises revenue.
A theatre sells 390 tickets per show at €10 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.
Full step-by-step solutions: practise this topic on examproblems.com.