Linear Modelling - Break Even Analysis
Interactive practice questions
Consider the following phone plans:
GO SMALL plan: This plan has a $\$20$$20 monthly base charge and charges $90$90 cents per minute for all calls.
GO MEDIUM plan: This plan has a $\$26$$26 monthly base charge and then charges $70$70 cents per minute for all calls.
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 | $\editable{}$ | $\editable{}$ |
Sketch the graph of the two plans.
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.
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 $\$700$$700 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.