4. Foster Foods, a large supermarket, has two types of checkout stands: those staffed with human workers (we will call these H), and those that are self-scanners (which we will call S). Human-operated checkout stands can check out 15 customers per hour, while self scanners check out 12 customers per hour.
a. Write the production function in terms of H and S, where q is the number of customers checked out per hour. How can we describe the inputs, H and S, given this functional form?
b. Suppose human checkout stands cost $30 per hour to operate (considering the human wage, plus operating costs for the equipment). Self scanners cost $20 per hour to operate. If our goal is to check out 400 customers per hour, what is the least expensive way to meet this goal? What is the total cost?