Question

A company produces a 3D modeling software program. The company uses the function below to estimate the weekly profits,
P
, in dollars, from selling
m
programs.



P
(
m
)
=
−
0
.
2
m
2
+
50
m
−
1320



Select TWO statements that are true according to the function.


The minimum weekly profit is $30.


The maximum weekly profit is $1,805.


The weekly profit will be $1,500 if the program costs $297.


The weekly profit will be less than zero if the program costs $20.


The weekly profit will be at a maximum if the program costs $220.

Answer 1

True statements:
- The maximum weekly profit is $1,805.
- The weekly profit will be less than zero if the program costs $20.

Work:
- Vertex at m = -b/(2a) = -50/(2·-0.2) = 125; P(125) = -0.2(125)^2 + 50(125) - 1320 = 1805 (maximum since a < 0).
- P(20) = -0.2(20)^2 + 50(20) - 1320 = -80 + 1000 - 1320 = -400 < 0.