8 A team of volunteers donates cakes for sale at a charity stall. The number of cakes that can be sold depends on the price. A model for this is \(\mathrm { y } = 190 - 70 \mathrm { x }\), where \(y\) cakes can be sold when the price of a cake is \(\pounds\) x.
- Find how many cakes could be given away for free according to this model.
The number of volunteers who are willing to donate cakes goes up as the price goes up. If the cakes sell for \(\pounds 1.20\) they will donate 50 cakes, but if they sell for \(\pounds 2.40\) they will donate 140 cakes. They use the linear model \(\mathrm { y } = \mathrm { mx } + \mathrm { c }\) to relate the number of cakes donated, \(y\), to the price of a cake, \(\pounds x\).
- Find the values of the constants \(m\) and \(c\) for which this linear model fits the two data points.
- Explain why the model is not suitable for very low prices.
- The team would like to sell all the cakes that they donate.
Find the set of possible prices that the cakes could have to achieve this.