Step-by-step explanation:
As you found in parts a and b, p = 840 − 2x, and R(x) = -2x² + 840x.
For part c, profit = revenue − cost.
P(x) = R(x) − C(x)
P(x) = -2x² + 840x − (2x² + 15x + 1500)
P(x) = -2x² + 840x − 2x² − 15x − 1500
P(x) = -4x² + 825x − 1500
The maximum profit is at the vertex of the parabola.
x = -b / (2a)
x = -825 / (2 × -4)
x = 103.125
Or, we can use calculus:
P'(x) = -8x + 825
0 = -8x + 825
x = 103.125
Rounding, the manufacturer should produce 103 refrigerators each week.
