math question need help

Question

Suppose the profit from the sale of x units of a product is P = 6400x − 18x² − 400.

(a) What level(s) of production will yield a profit of $120,400? (Enter your answers as a comma-separated list. Round your answers to two decimal places.)

x = 

 

(b) Can a profit of more than $120,400 be made?

YesNo    

Answer 1

Hi

The first part of the question is just asking you ... when you plug in a profit P = 120400 , what is x.

120400 = 6400 x - 18x² - 400 You can subtract over the 120400 and use the quadratic formula or just graph to find the roots. These roots will give you the x values that make this equation true....PRODUCTION IN THE QUESTION.

The solutions are x = 20 and x = 335.56

b) Can a profit of more than $120,400 be made? Well the graph of this function is a parabola that opens downward. Therefore, there is a max value....turning point ...which we can find in a variety of ways. This max tells us the maximum profit that can be achieved. You can use the axis of symmetry ... x = -b / 2a to find the max by plugging this value into the Profit equation or just find the maximum value use your graphing calculator.

The maximum profit is $568,488.89 and will be achieved when the production is at 177.78 items.

Hope this helps!

Kevin