A chef cooks different kinds of meat in a conventional oven. He has a chart that gives him the temperature and time to cook each kind of meat. He was cooking his meat this way for a number of years, but he was not satisfied with the quality of the product. Because of fluctuations in the oven temperature, the meat did not always cook to his satisfaction. To improve the situation, he recently outfitted his oven with a probe that he would insert into the meat. He would then set the oven temperature and the desired internal temperature of the meat. When the internal temperature of the meat as measured by the probe reached the target temperature, the oven would sound an alarm and turn itself off. With this new improvement he is lot happier with the quality of his cooked meats.

$($a$)$ Classify the mode of control employed by the chef as feedforward control or feedback control in each of the two cases $($before improvement and after improvement$).$

$($b$)$ For each case also specify which variables are controlled and manipulated variables.