A bakery sells Boston cream pies and carrot cakes. Each Boston cream pie requires 30 minutes preparation time, 30 minutes baking time, and 15 minutes for finishing. Each carrot cake requires 45 minutes preparation time, 50 minutes baking time, and 10 minutes for finishing.
(a) Write a matrix T representing the required time for preparation, baking, and finishing for the Boston cream pies and the carrot cakes.
(b) The bakery receives an order for 20 Boston cream pies and 8 carrot cakes for a large party. Find a matrix S so that either ST or TS gives the total preparation, baking, and finishing times required to fill this order.
(c) What is the total baking time? What is the total finishing time?