Domain and Range of the Cost Function

Domain: The domain of a function is the set of all possible values of the independent variable (Q in this case) for which the function is defined. The given cost function is C = 150 + 7Q. However, the firm has a capacity limit of 100 units of output per day. This means that the firm cannot produce more than 100 units of output. Therefore, the domain of the cost function is Q ≤ 100.

Range: The range of a function is the set of all possible values of the dependent variable (C in this case) that the function can take. The cost function is C = 150 + 7Q. Since the firm incurs a fixed cost of 150 per day, the minimum value of the cost function occurs when Q = 0. Therefore, the minimum value of C is 150. However, there is no upper limit on the cost since the firm can produce any number of units up to its capacity limit of 100 units. Therefore, the range of the cost function is C ≥ 150.

Explanation: The domain of the cost function is limited by the capacity of the firm, which is 100 units of output per day. This means that the firm cannot produce more than 100 units of output and, therefore, the cost function is only defined for values of Q that are less than or equal to 100. The range of the cost function is determined by the fixed cost of 150 and the fact that there is no upper limit on the cost since the firm can produce any number of units up to its capacity limit of 100 units. Therefore, the minimum value of the cost function is 150, and the cost can increase indefinitely as the firm produces more units up to its capacity limit.