Suppose you were a heating engineer and you wished to consider a house as a dynamic system. without a heater, the average temperature in the house would clearly vary over a 24-h period. what might you consider for inputs, outputs, and state variables for a simple dynamic model? how would you expand your model so that it would predict temperatures in several rooms of the house? how does the installation of a thermostatically controlled heater change your model?

$527.7.if the following was the question  $527.7 is the answer.students who are trying to raise funds have an agreement with a local pizza chain. the chain has agreed to sell them pizzas at a discount, which the students can then resell to families in the local community for a profit. it is expected that of the 500 families in the community, at most 70% will buy pizza. based on a survey of their personal preferences, the students believe that they should order no more than 120 cheese pizzas, no more than 150 pepperoni pizzas, and no more than 100 vegetarian pizzas. they also want to make sure that at least 20% of the total pizzas are cheese and at least 50% of the pizzas are pepperoni. they make a profit of $1.45, $1.75, and $1.98, respectively, for each cheese, pepperoni, and vegetarian pizza they resell. how many pizzas of each type should they buy?