Answer:
The reasonable amount is $3550 or greater
Step-by-step explanation:
Given
[tex]c=\$50[/tex] ---- shipping fee
[tex]r =\$35[/tex] --- unit selling price
[tex]n \to[/tex] number of orders
[tex]n \ge 100[/tex] ---- domain of order
Required
The reasonable ordering amount
The function for n calculator can be represented as:
[tex]f(n) = r * n + c[/tex]
This gives:
[tex]f(n)=35 * n + 50[/tex]
[tex]f(n)=35n + 50[/tex]
Recall that the domain is: [tex]n \ge 100[/tex]
So, we have:
[tex]f(n)=35n + 50[/tex] [tex]n \ge 100[/tex]
The reasonable amount of order implies that we calculate the range of the function
[tex]n \ge 100[/tex] implies that the minimum is 100
So:
Substitute 100 for n in [tex]f(n)=35n + 50[/tex]
[tex]f(100) = 35 * 100+50[/tex]
[tex]f(100) = 3500+50[/tex]
[tex]f(100) = 3550[/tex]
So, the range of the function is:
[tex]3550 \le f(n) < \infty[/tex]
