Question

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.

Answer 1

Answer:

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

Step-by-step explanation:

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

$C = C_{o} + C_{v}$ (1)

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

$C_{v} = C-C_{o}$

$C_{v} = \ \,300000 -\ \,50000$

$C_{v} = \ \,250000$

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

$C_{v} = r\cdot n$ (2)

Where:

$r$ - Production cost of a tire, in monetary units per tire.

$n$ - Amount of produced tires, in tires.

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

$n = \frac{C_{v}}{r}$

$n = \frac{\ \,250000}{\ \,1.20\,\frac{1}{tire} }$

$n = 208333\,tires$

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