Answer:
The level of wages that maximize tge profit is $61.257
And the correspond value for the profit is:
Explanation:
For this case we have the following function:
Where x represent the daily wages paid , and p(x) the profit, the objective is maximize this function, and in order to do this the first step is derivate the function respect to x and we got this:
As we can see we have a quadratic equation now we need to set up equal the derivate obtained to 0 and then solve for the critical points, like this:
We can use the quadratic formula given by:
And for this case a=0.003 , b=-1 , c =50
Replacing this we got :
And we got:
Now we need to find the second derivate, like this:
And we can replace the values obtained:
So then 61.257 is a maximum.
So then 272.076 is a minimum.
So then the level of wages that maximize tge profit is $61.257
And the correspond value for the profit is: