Optimization (Maxima and Minima) — Engineering Board Exam Practice Questions
24 free engineering board exam reviewer questions on Optimization (Maxima and Minima) (Differential Calculus), each with the correct answer and a worked solution.
- Find two positive numbers whose sum is 20 and whose product is a maximum.
- A farmer has 200 m of fencing to enclose a rectangular field bordered on one side by a river (no fence is needed along the river). Find…
- An open-top box is made by cutting equal squares of side x from each corner of a 12 in by 12 in sheet of cardboard and folding up the…
- A rectangular box with a square base and no top is to have a total surface area of 108 square inches. Find the maximum possible volume.
- A closed cylindrical can is to have a volume of 16π cubic inches. Find the radius that minimizes the total surface area.
- Find the point on the line y=2x+3 that is closest to the origin.
- A right circular cylinder is inscribed in a sphere of radius 6. Find the height of the cylinder that maximizes its volume.
- A wire 100 cm long is cut into two pieces. One piece is bent into a square and the other into a circle. How many centimeters of wire…
- An open rectangular box with a square base is to have a volume of 32 cubic feet. Find the dimensions that minimize the amount of material…
- A Norman window (a rectangle surmounted by a semicircle) is to have a perimeter of 20 ft. Find the radius of the semicircle that maximizes…
- A cone-shaped paper cup is to hold 100 cm3 of water. Find the height that minimizes the amount of paper needed to make the cup (i.e…
- A page is to contain 24 in2 of print. The margins at the top and bottom are 1.5 in each, and at the sides 1 in each. Find the dimensions…
- Find the maximum area of a rectangle that can be inscribed in a semicircle of radius 5, with one side on the diameter.
- A closed box with a square base is to have a surface area of 150 square inches. Find the dimensions that maximize the volume.
- The sum of the base and height of a triangle is 20 cm. Find the height that maximizes the area of the triangle.
- A manufacturer determines that the profit from producing x units of a product is P(x)=-2x2+800x-15000 pesos. Find the number of units that…
- Find the minimum value of f(x)=x2-6x+13.
- A rectangular field is to be enclosed by a fence and divided into two equal parts by another fence parallel to one pair of sides. If 600 m…
- A wire 36 cm long is bent to form a rectangle. Find the dimensions of the rectangle with maximum area.
- Find the point on the curve y=x2 that is closest to the point (3,0).
- A company's total cost function is C(x)=0.02x2+30x+5000, and its price function is p(x)=150-0.04x (both in pesos, x = units). Find the…
- Find the maximum area of a rectangle that can be inscribed in a circle of radius 4.
- A rectangular sheet of metal 12 inches wide is bent to form an open rectangular channel by turning up two sides of equal height x. Find…
- The strength of a rectangular beam varies as the product of its width and the square of its depth. Find the width of the strongest beam…