Furniture store opening special:
As part of their opening special, a furniture store has promised to give away at least prizes with a total value of at least . They intend to give away kettles and toasters. They decide there will be at least units of each prize. A kettle costs the company and a toaster costs .
Determine how many of each prize will represent the cheapest option for the company. Calculate how much this combination of kettles and toasters will cost.
Use a suitable strategy to organise the information and solve the problem.
In this situation there are two variables that we need to consider: let the number of kettles produced be and let the number of toasters produced be .
Write down a summary of the information given in the problem so that we consider all the different components in the situation.
Use the summary to draw up a table of the number of kettles and toasters that are needed. We will consider multiples of 5 to simplify the calculations:
We need to have at least kettles and toasters together.
With this limitation, we are able to eliminate some of the combinations in the table where :
These combinations have been excluded as possible answers.
We can express the minimum cost as: .
By substituting the different combinations for and , we can find the value that gives the minimum cost.
We are looking for a pair of values that give the minimum cost. We can easily check the non-multiples of 5 for kettles and toasters to confirm that kettles and toasters meet the minimum cost.
For example if kettles and toasters are given away, the cost will be . And if kettles and toasters are given away, the cost will be .
The minimum cost of can be obtained if kettles and toasters are given away. This will result in a cost of .