New Zealand
Level 8 - NCEA Level 3

# Linear Modelling - Break Even Analysis

## Interactive practice questions

Consider the following phone plans:

GO SMALL plan: This plan has a $\$20$$20 monthly base charge and charges 9090 cents per minute for all calls. GO MEDIUM plan: This plan has a \26$$26 monthly base charge and then charges $70$70 cents per minute for all calls.

a

Complete the following table of values for various total monthly call times for the two plans:

Call time (in minutes) Total cost for GO SMALL plan Total cost for GO MEDIUM plan
$20$20 $\editable{}$ $\editable{}$
$30$30 $\editable{}$ $\editable{}$
$40$40 $\editable{}$ $\editable{}$
$50$50 $\editable{}$ $\editable{}$
b

Sketch the graph of the two plans.

c

Using the graphs, determine how many minutes of calls would need to be made so that the monthly bill costs the same on both plans.

Easy
Approx 7 minutes

The cost of manufacturing toys ($C$C) is related to the number of toys produced ($n$n) by the formula $C=400+2n$C=400+2n. The revenue ($R$R) made from selling $n$n toys is $R=4n$R=4n.

The cost for a furniture manufacturer to make a dining table is $\$450$$450 per dining table plus a fixed setup cost of \6000$$6000. The dining tables will sell for $\$700700 each.

This graph shows the cost $C\left(x\right)$C(x), the revenue $R\left(x\right)$R(x) and the profit $P\left(x\right)$P(x) from making and selling $x$x units of a certain good.

### Outcomes

#### M8-4

Use curve fitting, log modelling, and linear programming techniques

#### 91574

Apply linear programming methods in solving problems