Question

A company in its first year of business produced 150 training manuals for a total cost of $2.350. The following

year, the company produced 50 more manuals at a cost of $ 1,450. Use this information to find a linear equation
that gives the total cost of producing training manuals from the number of manuals produced.

Answer 1

y = 9x +1000

Explanation:

The relation for the total cost of manuals based on the number produced will be the sum of a base cost and a variable cost. The variable cost is the product of the cost per manual and the number of manuals.

Cost per manual

The cost per manual can be found by looking at the increase in cost relative to the increase in the number of manuals produced:

cost per manual = (increase in cost)/(increase in production)

= ($2350 -1450)/(150 -50) = $900/100 = $9

Base cost

The base cost will be added to the product of the cost per manual and the number of manuals. For the 2nd year purchase, this is ...

$1450 = base cost + (50 manuals)×($9/manual)

$1450 = base cost + $450

base cost = $1450 -450 = $1000

Equation

The equation for the cost in dollars (y) of producing x manuals can now be described by ...

y = (cost per manual)x +(base cost)

y = 9x +1000