Question

Pauline, Patricia and Polly are pie bakers at their bakery, Perfect Pies. They bake four different pie flavors: cherry, blueberry, apple and pecan. I understand question #1 but I need someone to help with questions 2-6 please.

Answer 1

The answer is given below

Explanation:

1) The persons are given by the matrix:

The number of different pie flavours is given by the matrix:

`n=\left[\begin{array}{cccc}3&4&1&1\\6&6&4&6\\2&2&5&4\end{array}\right]`

The cost of ingredients for each pie is given by the matrix:

`I=\left[\begin{array}{ccc}3\\5\\2\\6\end{array}\right]`

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]`

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]`

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]`

The price of pie at Sugary Sarah is represented by the matrix:

`SS=\left[\begin{array}{ccc}8\\9\\8\\13\end{array}\right]`

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]`

5) Patricia yielded the greatest income. She made $208 + $212 = $420

6) Polly made $126 from selling at Sugary Sarah