Final answer:
The domain for the function modeling profit based on the number of small square pizzas sold by the CTW Pizza Company is all non-negative integers, and the range is all non-negative multiples of $3, corresponding to the profits earned from selling the pizzas. Additionally, the quantity demanded equation confirms that at a price of $2, the demand equates to the supply of 12 pizzas.
Step-by-step explanation:
The CTW Pizza Company has decided to sell small square pizzas at a cost of $2.00 for production and at a selling price of $5.00 each. To find the domain and range for the function that models the relationship between profit and the number of pizzas sold, we first need to establish the profit function. The profit per pizza is calculated by subtracting the cost from the selling price, which is $5.00 - $2.00 = $3.00 per pizza.
The domain of this function represents the possible number of pizzas sold, which can be any non-negative integer (since you cannot sell a negative number of pizzas and you cannot sell a fraction of a pizza). This means the domain is all non-negative integers (0, 1, 2, 3, ...).
The range of the function is the set of all possible profits. If P represents the profit and x represents the number of pizzas sold, the profit function is P(x) = 3x. Since the company cannot sell a negative number of pizzas, the range is all non-negative multiples of 3 (0, 3, 6, 9, ...), corresponding to the profit earned from selling 0, 1, 2, 3, ... pizzas respectively.
To consider the demand equation Qd = 16 - 2P, where P is the price in dollars and Qd is the quantity demanded, we notice that when the price is set at $2, the quantity demanded is Qd = 16 - 2*2 = 12 pizzas. This correlates with the supply equation, indicating that the company is indeed matching the quantity demanded at this price point, which is integral to economic decision-making.
Therefore, in this case, both the domain and range are sets of non-negative integers, with the domain being intuitively larger since it represents the possible quantity of pizzas sold, and the range being specifically the profits in increments of $3.00.