Help Please I am struggling with a math problem

Question

For a certain company, the cost for producing x𝑥 items is 40x+300and the revenue for selling x𝑥 items is 80x−0.5^2

 

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 x𝑥  that will create a profit of $300

 

The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2;4;62;4;6 or x+1;x−1𝑥+1;𝑥−1). The order of the list does not matter. To enter a−−√𝑎, type sqrt(a).

 

x=

 

Part c: Is it possible for the company to make a profit of $15,000?

Answer 1

Profit = P= R-C = 40x- 300.25 IF your little Xx means just x

or maybe you left out an x in the squared term which should read -.5x^2?

then P=-.5x^2 +40x - 300

300 =-.5x^2 +40x -300

.5x^2 -40x + = 0

x^2 -80x +1200 = 0, factor, complete the square or use the quadratic formula

to find x that gives profit of 300

(x-40)^2 = 400

x = 40+/-20 = 20 or 60

max profit is when P'=0 = -x +40=0, when x=40

when x= 40, P =-800 +1600 -300 = 1100

15000 is Not possible