A tech startup was founded in 2021 and needs to hire the following numbers of software engineers over the next five years: Year 2022 2023 2024 2025 2026 # of software engineers 110 130 70 165 50 Since the demand for software engineers fluctuates and the startup aims to introduce new products to market as quickly as possible, it may be more practical to keep more engineers than needed during some years of the planning horizon. The startup estimates that the cost of recruiting and maintaining the software engineers is a function of their length of stay with the company. The following table summarizes these estimates: Length of employment (# of years) 1 2 3 4 5 Cost per software engineer 140 170 230 250 110 The startup is interested in the recruiting schedule to minimize the total cost. (Hint: Think about the number of software engineers the startup needs to hire for different horizons 1, 2, 3, 4, 5 years - in each year of the planning horizon.) (a) (15 points) Write the problem as an optimization problem. You can ignore the fact that the numbers of engineers cannot take fractional values. (b) (20 points) Determine the optimal solution by using Excel's solver or Python's packages. If you use Excel, be sure to submit the Excel sheet and solver window. If you use Python, be sure to submit your fully commented code and output.