Question 1157181
r(x) = 1200x - x^2
c(x) = 3000 + 20x
p(x) = r(x) - c(x)
that becomes:
p(x) = 1200x - x^2 - (3000 + 20x)
simplify to get:
p(x) = 1200x - x^2 - 3000 - 20x
combine like terms to get:
p(x) = -3000 + 1180x - x^2
order the terms in descending order of degree to get:
p(x) = -x^2 + 1180x - 3000
a = the coefficient of the x^2 term = -1
b = the coefficient of the x term = 1180
c = the constant term = -3000
the maxim profit is when x = -b/2a.
that becomes x = -1180/-2 = 590.
the maximum profit is the value of the equation at x = 590
that becomes p(x) = 345,100
that's your solution.
here's the graph that confirms that.
<img src = "http://theo.x10hosting.com/2020/042601.jpg" alt="$$$" >