4. (30 points) A think tank uses data scientists (D) and economists (E) to produce reports for government agencies. The number of reports the think tank produces is given by the following production function: f(D,E) =12D3E3 (3) Data scientists make twice as much as economists. Hiring a new data scientist costs $400 while hiring a new economist only costs $50 (an absolute bargain). Currently, the think tank has 8 data scientists. They are under long contracts so the think tank cannot fire them. Additionally, due to a shortage of data scientists around the country, the think tank cannot currently hire any additional data scientists. They haven't hired any economists yet but can quickly find as many as they want. () (b) (c) If the think tank can sell each of its reports for $40, how many economists should the think tank hire during this period when it cannot adjust the number of data scientists? Write down a function that gives the total costs of producing R reports while the firm cannot adjust the number of data scientists. Your cost function should contain only numerical constants and R. Now William & Mary expands its data science program as do many other universities. There are plenty of data scientists to hire and the firm's contracts with its initial data scientists have all expired. The think tank can now use any combination of data scientists and economists it wants. Find expressions for the optimal number of data scientists and optimal number of economists to hire in terms of the desired number of reports (D(R) and E(R)). Write down a function giving the minimum total costs of producing R reports now that the think tank can hire any combination of data scientists and economists. This cost function should contain only R and numerical constants. On a graph with R on the horizontal axis and dollars on the vertical axis, graph the average cost curves for the think tank in both the short and long term, labelling which is which