Answer:
The answer is given below
Step-by-step explanation:
1) The persons are given by the matrix:
The number of different pie flavours is given by the matrix:
The cost of ingredients for each pie is given by the matrix:
![I=\left[\begin{array}{ccc}3\\5\\2\\6\end{array}\right]](https://tex.z-dn.net/?f=I%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C5%5C%5C2%5C%5C6%5Cend%7Barray%7D%5Cright%5D)
2)
![\left[\begin{array}{ccc}Pauline\\Patricia\\Polly\end{array}\right] =\left[\begin{array}{cccc}3&4&1&1\\6&6&4&6\\2&2&5&4\end{array}\right] \left[\begin{array}{ccc}3\\5\\2\\6\end{array}\right] \\\left[\begin{array}{ccc}Pauline\\Patricia\\Polly\end{array}\right] =\left[\begin{array}{ccc}37\\92\\50\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7DPauline%5C%5CPatricia%5C%5CPolly%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D3%264%261%261%5C%5C6%266%264%266%5C%5C2%262%265%264%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C5%5C%5C2%5C%5C6%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7DPauline%5C%5CPatricia%5C%5CPolly%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D37%5C%5C92%5C%5C50%5Cend%7Barray%7D%5Cright%5D)
3) The cost of pie for Patricia = $92
The total cost of pie for all bakers = 37 + 92 + 50 = $179
The ratio of cost of Patricia pie to that of all three bakers = $92/$179 = 0.514
Patricia pie cost of ingredients is more than half of that of all three bakers
4)
The price of pie at Samuels sweet is represented by the matrix:
![SA=\left[\begin{array}{ccc}8\\10\\7\\12\end{array}\right]](https://tex.z-dn.net/?f=SA%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%5C%5C10%5C%5C7%5C%5C12%5Cend%7Barray%7D%5Cright%5D)
The income of each baker made by selling at samuels sweets is:
![\left[\begin{array}{ccc}Pauline\\Patricia\\Polly\end{array}\right] =\left[\begin{array}{cccc}3&4&1&1\\6&6&4&6\\2&2&5&4\end{array}\right] \left[\begin{array}{ccc}8\\10\\7\\12\end{array}\right] \\\left[\begin{array}{ccc}Pauline\\Patricia\\Polly\end{array}\right] =\left[\begin{array}{ccc}83\\208\\119\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7DPauline%5C%5CPatricia%5C%5CPolly%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D3%264%261%261%5C%5C6%266%264%266%5C%5C2%262%265%264%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%5C%5C10%5C%5C7%5C%5C12%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7DPauline%5C%5CPatricia%5C%5CPolly%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D83%5C%5C208%5C%5C119%5Cend%7Barray%7D%5Cright%5D)
The price of pie at Sugary Sarah is represented by the matrix:
![SS=\left[\begin{array}{ccc}8\\9\\8\\13\end{array}\right]](https://tex.z-dn.net/?f=SS%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%5C%5C9%5C%5C8%5C%5C13%5Cend%7Barray%7D%5Cright%5D)
The income of each baker made by selling at Sugary Sarah is:
![\left[\begin{array}{ccc}Pauline\\Patricia\\Polly\end{array}\right] =\left[\begin{array}{cccc}3&4&1&1\\6&6&4&6\\2&2&5&4\end{array}\right] \left[\begin{array}{ccc}8\\9\\8\\13\end{array}\right] \\\left[\begin{array}{ccc}Pauline\\Patricia\\Polly\end{array}\right] =\left[\begin{array}{ccc}81\\212\\126\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7DPauline%5C%5CPatricia%5C%5CPolly%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D3%264%261%261%5C%5C6%266%264%266%5C%5C2%262%265%264%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%5C%5C9%5C%5C8%5C%5C13%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7DPauline%5C%5CPatricia%5C%5CPolly%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D81%5C%5C212%5C%5C126%5Cend%7Barray%7D%5Cright%5D)
5) Patricia yielded the greatest income. She made $208 + $212 = $420
6) Polly made $126 from selling at Sugary Sarah