i need help solving this thank you so much

Question

or a certain company, the cost for producing xx items is 35x+300 and the revenue for selling xx items is 75x−0.5

 

The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit!

 

Part a: Set up an expression for the profit from producing and selling xx items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)

 

Part b: Find two values of x that will create a profit of $50

 

 

Part c: Is it possible for the company to make a profit of $2,500?

Answer 1

P = R-C = 75x -0.5 - (35x +300) = 40x -300.5

maximum profit is x = infinity, the more sold the more the profit

but

if by "xx" you mean x times x = x^2, then maybe you intended to write

R-C = 40x^2 -300.5, but the max profit level is still infinite

Maybe you meant to write an x^2 term

such as

P= -x^2 +40x -300.5

then profit maximizing level is x= 20

with max P = $499.50

P=$50 when -x^2 +40x -300.5 = 50

when x^2 -40x + 350.5 = 0

x= 40/2 + or - (1/2)sqr(40^2 -4(350.5))

x = about 20+ or - 7.04

x = about 27 or 13 for $25 profit

$2,500 is not possible as $499.50 is the max profit possible