The monthly profit from the sale of a product is given by the equation:\[ P = 16x - 0.1x^2 - 200 \] dollars.(a) What level of production maximizes profit?\[ \_\_\_\_ \] units(b) What is the maximum possible profit?\[ \$\_\_\_\_ \]**Explanation:**- The equation represents a quadratic function where $ P $ is the profit, and $ x $ is the number of units produced.- To find the level of production that maximizes profit, determine the vertex of the parabola, since this is a downward-opening parabola (the coefficient of $ x^2 $ is negative).- The maximum profit can be calculated by substituting the value of $ x $ that maximizes profit back into the profit equation.

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The monthly profit from the sale of a product is given by P = 16x – 0.1x2 – 200 dollars. (a) What level of production maximizes profit? units (b) What is the maximum possible profit?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

The monthly profit from the sale of a product is given by the equation:

\[ P = 16x - 0.1x^2 - 200 \] dollars.

(a) What level of production maximizes profit?
\[ \_\_\_\_ \] units

(b) What is the maximum possible profit?
\[ \$\_\_\_\_ \]

**Explanation:**
- The equation represents a quadratic function where $ P $ is the profit, and $ x $ is the number of units produced.
- To find the level of production that maximizes profit, determine the vertex of the parabola, since this is a downward-opening parabola (the coefficient of $ x^2 $ is negative).
- The maximum profit can be calculated by substituting the value of $ x $ that maximizes profit back into the profit equation.

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