Question

Mr Kent sells calculators for $35 each. If an order is placed from a business account, there is a $50 shipping fee, and no fewer than 100 calculators can be purchased. Which is a reasonable amount of money that a business would spend when ordering calculators?

Answer 1

The reasonable amount is $3550 or greater

Explanation:

Given

`c=\$50` ---- shipping fee

`r =\$35` --- unit selling price

`n \to` number of orders

`n \ge 100` ---- domain of order

Required

The reasonable ordering amount

The function for n calculator can be represented as:

`f(n) = r * n + c`

This gives:

`f(n)=35 * n + 50`

`f(n)=35n + 50`

Recall that the domain is:
`n \ge 100`

So, we have:

`f(n)=35n + 50`
`n \ge 100`

The reasonable amount of order implies that we calculate the range of the function

`n \ge 100` implies that the minimum is 100

So:

Substitute 100 for n in
`f(n)=35n + 50`

`f(100) = 35 * 100+50`

`f(100) = 3500+50`

`f(100) = 3550`

So, the range of the function is:

`3550 \le f(n) < \infty`