Question

When X units of a certain are made and sold in a year, the yearly profit is P(x)=-40,255+9.8x dollars. What level of production and sales give a yearly profit of more than $84,355?

Answer 1

The level of production and sales that give a yearly profit of more than $84,355 is 12,715 units.

To determine the level of production and sales that give a yearly profit of more than $84,355, we need to set up an inequality using the profit function. The inequality would be P(x) > 84,355. Substituting P(x)=-40,255+9.8x into the inequality, we get:

-40,255+9.8x > 84,355

To solve this inequality, we need to isolate the x variable. We can start by adding 40,255 to both sides of the inequality:

9.8x > 124,610

Next, we divide both sides of the inequality by 9.8 to solve for x:

x > 12,714.29

Rounding up to the nearest whole number, the level of production and sales that give a yearly profit of more than $84,355 is 12,715 units.