Final answer:
The total cost of production for the technology that minimizes the firm's cost cannot be determined precisely without knowing the exact mix of receptionists and computers. However, by analyzing previous examples provided, a higher number of computers becomes more cost-efficient as the wages of receptionists increase.
Step-by-step explanation:
Understanding Cost-Minimizing Production Technology
To determine the technology that minimizes the firm's costs of production, we need to compare the total costs for live receptionists and computers for client self-check-in. In this scenario, the cost of a receptionist is $120 per worker per day, and the cost of a computer is $50 per computer. However, the information provided does not specify the number of workers or computers needed. Thus to proceed, we would need additional information such as the number of receptionists and computers the fitness center is considering.
In the examples given, we observe that when worker wages were $40, and computer costs were $80, technology 1 with more workers was the low-cost option. As the wage rate increased to $55, technology 2 became more cost-efficient. Finally, when wages reached $90 and the cost of computers remained the same, technology 3, which likely involves a higher number of computers and fewer workers, becomes the most cost-effective option.
To determine the total cost of production for the technology that minimizes costs in our student's scenario, we would need information on the optimal mix of live receptionists and computers dictated by the firm's production needs and constraints, which is not provided in the question. Once that information is known, the calculation would be straightforward - summing the product of the number of receptionists and the cost per receptionist with the product of the number of computers and the cost per computer.