A rectangular pen is fenced with 48 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 20 cm × 32 cm by cutting equal squares of side x from the four corners and folding up the sides. Find the cut x that gives the largest volume.
An open box (no lid) with a square base must hold 13500 cm³. Use the least possible material, that is the smallest area of the base plus the four sides. Find the base side x.
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 smallest possible surface area A.
A theatre sells 240 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 maximum revenue R per show.
A company sells q units per week. The price at which it can sell them is p = 190 − 0.2q euros per unit, and the cost is C(q) = 700 + 160q euros. Find the price p that maximises profit.
Full step-by-step solutions: practise this topic on examproblems.com.