We want to optimize an investment strategy for Start Oil Company. Star Oil Company is considering five different investment opportunities. The cash outflows and net present values (in millions of dollars) are given in the following table. Cash Flows and Net Present Value for Investments in Capital Budgeting Investment ($) 1 2. 3 4 5 53 5 5 29 Time 0 cash outflow Time 1 cash outflow NPV 11 3 13 6 16 5 16 1 14 34 39 Star Oil has $40 million available for investment now (time 0) It estimates that one year from now (time1) $20 million will be available for investment. Money left over at time 0 cannot be used at time 1. Star Oil may purchase any fraction of each investment. In this case, the cash outflows and NPV are adjusted accordingly. For example, if Star Oil purchases one-fifth of investment 3, then a cash outflow of 1/5*5 = $1 million would be required at time 0, and a cash outflow of $1 million would be required at time 1. The one-fifth share of investment 3 would yield an NPV of 1/5*16 = $3.2 million. You cannot purchase more than 100% of any investment. o . Write the constraint equations for this problem, in terms of (X1, X2, X3, X4, Xs) where each x is the percentage of each investment that Start Oil will purchase. Write a function in Python that checks if a given solution for (X1, X2, X3, X4, Xs) is valid. Write a function in Python that computes the total return on investment for a given solution (X1, X2, X3, X4, Xs). It can assume that the solution is valid