The number of days the company earns a profit is the second day till the 7th day
<h3>How to determine the number of days the company earns a profit?</h3>
From the question, we have the following functions that can be used in our computation:
Cost function, C(x) = 2x2 – 20x + 80
Revenue function, R(x) = –x2 + 5x + 58
These functions can be properly represented as
Cost function, C(x) = 2x² – 20x + 80
Revenue function, R(x) = –x² + 5x + 58
When the company makes a profit, the revenue of the company exceeds the cost
This means that
R(x) > C(x)
Substitute the known values in the above equation, so, we have the following representation
–x² + 5x + 58 > 2x² – 20x + 80
Evaluate the like terms
–3x² + 25x - 22 > 0
Expand
–3x² + 3x + 22x - 22 > 0
Factorize the inequality
–3x(x - 1) + 22(x - 1) > 0
So, we have
(-3x + 22)(x - 1) > 0
This gives
-3x + 22 > 0 and x - 1 > 0
Evaluate
-3x > -22 and x > 1
Divide
x < 7.3 and x > 1
This can be combined as
1 < x ≤ 7
Hence, the company makes profit from the second day till the 7th day
Read more about profit functions at
brainly.com/question/25638609
#SPJ1
