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A company that produces healthcare services (patient visits) operates with the following production function where g 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: g = L[I'.H KD-EE} 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. [20pts] For the following questions, for simplicity, assume that w=1 and r=1. 2) Suppose the firm aims to produce eight visits this week (gq=8), calculate the optimal hours of human intelligence L and artificial intelligence K. Also find the total cost of producing those eight patient visits. [5 pts] 3) Considering the firm has the flexibility to adjust L and K (we are in the long run of the firm), what is the firm's supply curve? [Spts] 4) Suppose the firm decides on a new production level of 12 patients seen per week but has already committed to 9 hours of artificial intelligence K and cannot change this input. How many hours of human intelligence L will the firm need to employ to achieve this new production level in the short run of the firm? What will be the cost of reaching this new output? [Spts] 5) Intuitively, with words, briefly discuss what would happen with your answers in (1), and (2) if there is technological change and now the production function becomes: g = L0-25 0.5 [5pts]