Answer:
- 24 tables, correct
- $294 per day
Explanation:
Given the profit function P(x) = -6x² +288x -3162, you want to find the value of x and the value of P(x) corresponding to maximum profit.
Vertex
The vertex of the parabola described by ax²+bx+c lies on the line of symmetry:
x = -b/(2a)
This will be the value of x that is a maximum when a < 0.
The value of the function at that point can be found by evaluating the quadratic expression for the value of x just found.
Application
Maximum profit is had when ...
x = -(288)/(2(-6)) = 24
That maximum profit is ...
P(24) = (-6(24) +288)(24) -3162 = 144(24) -3162 = 294
For maximum profit, 24 tables should be made per day. The maximum profit is $294 per day.