Engineering Board Exam Reviewer · Optimization (Maxima and Minima) · medium
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 of the page that minimize the amount of paper used.
- 6 in x 9 in
- 8 in x 6 in
- 5 in x 10 in
- 4 in x 9 in
Answer
A. 6 in x 9 in
Solution
Let x,y be the print width and height, xy=24. Page area A=(x+2)(y+3)=(x+2)≤ft(24/x+3 )=30+3x+48/x. A'=3-48/x2=0 x=4, y=6. Page dimensions: (4+2)×(6+3)=6×9.
More Optimization (Maxima and Minima) questions
- 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.