Engineering Board Exam Reviewer · Optimization (Maxima and Minima) · easy

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 maximizes profit.

  1. 200 units
  2. 400 units
  3. 100 units
  4. 150 units

Answer

A. 200 units

Solution

P'(x)=-4x+800=0 x=200.

More Optimization (Maxima and Minima) questions

  1. Find the minimum value of f(x)=x2-6x+13.
  2. 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…
  3. A wire 36 cm long is bent to form a rectangle. Find the dimensions of the rectangle with maximum area.
  4. Find the point on the curve y=x2 that is closest to the point (3,0).
  5. 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…
  6. Find the maximum area of a rectangle that can be inscribed in a circle of radius 4.
  7. 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…
  8. 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…
  9. Find two positive numbers whose sum is 20 and whose product is a maximum.
  10. 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…

All Optimization (Maxima and Minima) questions