(Solved): You can use Maxima to do the matrix arithmetic in this question, or you can do it by hand. If you u ...
You can use Maxima to do the matrix arithmetic in this question, or you can do it by hand. If you use Maxima, then you do not need to include a printout or screenshot, but you must include sufficient details in your solution to make it clear what calculations Maxima has done. Games Ltd., a shop that sells different kinds of games, has decided to run a survey with their customers. They carried out the survey using three different methods: on Social Media, at the Shopping Centre, and by Email. Of the customers who were surveyed on Social Media,
30%prefer shopping In -Store and
70%prefer shopping Online. Of the customers who were surveyed at the Shopping Centre,
90%prefer shopping In-Store and
10%prefer shopping Online. Of the customers who were surveyed via Email,
40%prefer shopping In -Store and
60%prefer shopping Online. (a) (i) Write down the matrix that represents this network. (ii) Suppose that 2500 customers were surveyed on Social Media, 1800 at the Shopping Centre, and 2700 customers via Email. Use your matrix from part (i) to calculate the number of customers who prefer shopping In-Store and the number of customers who prefer shopping Online. (b) Suppose that: Of the customers who prefer shopping In-Store,
30%of them want to buy Adventure games,
50%want to buy Board games, and
20%want to buy Card games. Of the customers who prefer shopping Online,
40%of them want to buy Adventure games,
10%want to buy Board games, and
50%want to buy Card games. (You may assume that each customer only wants to buy one kind of game). (i) Draw a network diagram with input nodes P and Q , and output nodes A (Adventure games), B (Board games), and C (Card games), that represents the proportion of customers shopping Online and In-Store who want to buy the three kinds of games. (ii) Write down the matrix that represents this network. (iii) Hence find the single matrix that represents the proportion of surveyed customers, via Social Media, the Shopping Centre, and Email, who want to buy each kind of game, Adventure games, Board games, and Card games. (iv) Games Ltd. are about to run a huge marketing campaign via Social Media to increase sales of their products. State which kind of game they should expect to sell the most of during this campaign, and explain why.
