maximum profit 9.5 15

Question

The daily profit P in dollars of a company making tables is described by the function (x)=−6x2+288x−3162?,
where x is the number of tables that are manufactured in 1 day. The maximum profit of the company occurs at the vertex of the parabola. How many tables should be made per day in order to obtain the maximum profit for the? company? What is the maximum? profit?

Answer 1

P(x) = -6x² + 288x -3162

       = -6(x² - 48x) - 3162

       = -6(x2 -48x + 24²⁾ + 6*24² - 3162

       = 294 -6(x - 24)²

 

From this the vertex is (24, 294), which means

24 chairs made maximum the profit to be $294

Answer 2

The x coordinate of the vertex is -b/2a from the

quadratic equation.

 

a = -6,  b = 288

 

-b/2a = -288/-12 = 24 tables

 

The y coordinate is f(24)

-6(24)² + 288(24) - 3162

= -6(576) + 6912 - 3162

= 294

 

The maximum daily profit is $294 from making 24 tables