A certain office can purchase a photocopier for $5600 with a maintenance fee of $15 a month. On the other hand, they can rent the photocopier for $95 a month (including maintenance). If they purchase the photocopier, each copy would cost 3¢; if they rent, the cost is 6¢ per copy. The office manager estimates that they make 8000 copies a month.
(a) Find a linear function C that models the cost
C(x)
(in dollars) of purchasing and using the copier for x months.
(b) Find a linear function S that models the cost
S(x)
(in dollars) of renting and using the copier for x months.
I'm looking for the answer not another question
To find the linear functions C(x) and S(x) that model the cost of purchasing and renting the copier respectively, we need to consider the initial cost, the monthly maintenance fee, and the cost per copy.
(a) Cost function C(x) - purchasing and using the copier:
The initial cost of purchasing the copier is $5600. Since the maintenance fee is $15 a month, the total monthly cost for maintenance will be 15 * x, where x is the number of months.
The cost per copy is 3¢, or $0.03. Since the office makes 8000 copies per month, the total cost for copies will be 0.03 * 8000 * x = 240 * x.
Therefore, the linear cost function C(x) can be found by adding all these costs together:
C(x) = 5600 + 15x + 240x
Simplifying the expression, we get:
C(x) = 5600 + 255x
(b) Cost function S(x) - renting and using the copier:
The monthly cost for renting, including maintenance, is $95. Since the office makes 8000 copies per month, the total cost for copies will be 0.06 * 8000 * x = 480 * x.
Therefore, the linear cost function S(x) can be found by adding the renting cost and the cost per copy together:
S(x) = 95 + 480x
So, the linear functions that model the cost of purchasing and renting are:
(a) C(x) = 5600 + 255x
(b) S(x) = 95 + 480x