A car manufacturing firm wishes to introduce a new line of tires into its product range. It costs them $50,000 to introduce the new line, and $1.20 per tire. If they have a budget of $300,000 to introduce the new line, how many tires can they make? Give your answer to the nearest thousand.

The total budget ([tex]C[/tex]), in monetary units, is the sum of fixed costs (cost of introducing the new line) ([tex]C_{o}[/tex]), in monetary units, and variable costs (cost of producing tires) ([tex]C_{v}[/tex]), in monetary units:

[tex]C = C_{o} + C_{v}[/tex] (1)

If we know that [tex]C = \$\,300000[/tex] and [tex]C_{o} = \$\,50000[/tex], then variable costs are:

[tex]C_{v} = C-C_{o}[/tex]

[tex]C_{v} = \$\,300000 -\$\,50000[/tex]

[tex]C_{v} = \$\,250000[/tex]

And the variable cost can be defined by the following formula:

[tex]C_{v} = r\cdot n[/tex] (2)

Where:

[tex]r[/tex] - Production cost of a tire, in monetary units per tire.

[tex]n[/tex] - Amount of produced tires, in tires.

If we know that [tex]C_{v} = \$\,250000[/tex] and [tex]r = \$\,1.20\,\frac{1}{tire}[/tex], then the amount of produced tires:

[tex]n = \frac{C_{v}}{r}[/tex]

[tex]n = \frac{\$\,250000}{\$\,1.20\,\frac{1}{tire} }[/tex]

[tex]n = 208333\,tires[/tex]

208333 tires can be made with a budget of $ 300000.