A company that produces healthcare services (patient visits) operates with the following production function where q denotes the weekly output level in terms of the number of patients, L represents the hours of human intelligence (doctors and nurses) employed per week, and K denotes the hours of artificial intelligence utilized per week: q=L0.5 K0.25 The cost per hour for artificial intelligence is represented by r, and the cost per hour for human intelligence is denoted by w, both expressed in dollars per hour. 1) Determine the optimal levels of L and K that minimize the firm's costs given a target level of production q. Express the cost-minimizing levels of L and K as two functions of q, w, and r. Show your work carefully. For the following questions, for simplicity, assume that w=1 and r=1. 2) Suppose the firm aims to produce eight visits this week (q=8), calculate the optimal hours of human intelligence L and artificial intelligence K. Also find the total cost of producing those eight patient visits.

A company that produces healthcare services (patient visits) operates with the following production function where q denotes the weekly output level in terms of the number of patients, L represents the hours of human intelligence (doctors and nurses) employed per week, and K denotes the hours of artificial intelligence utilized per week: q=L0.5 K0.25 The cost per hour for artificial intelligence is represented by r, and the cost per hour for human intelligence is denoted by w, both expressed in dollars per hour. 1) Determine the optimal levels of L and K that minimize the firm's costs given a target level of production q. Express the cost-minimizing levels of L and K as two functions of q, w, and r. Show your work carefully. For the following questions, for simplicity, assume that w=1 and r=1. 2) Suppose the firm aims to produce eight visits this week (q=8), calculate the optimal hours of human intelligence L and artificial intelligence K. Also find the total cost of producing those eight patient visits.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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