HiRise Construction can bid on two 1-year projects. The following table provides the quarterly cash flow (in millions of dollars) for the two projects.

HiRise has cash funds of $1 million at the beginning of each quarter and may borrow at most $1 million at a 10% nominal annual interest rate. Any borrowed money must be returned at the end of the quarter. Surplus cash can earn quarterly interest at an 8% nominal annual rate. Net accumulation at the end of one quarter is invested in the next quarter.

(a) Assume that HiRise is allowed partial or full participation in the two projects. Determine the level of participation that will maximize the net cash accumulated on December 31. Solve the model using Solver of AMPL.

(b) Is it possible in any quarter to borrow money and simultaneously end up with surplus funds? Explain.

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Project I II January 1 -1.0 -3.0 Cash flow (in millions of $) at July 1 October 1 -1.5 1.8 1.5 1.8 April 1 -3.1 -2.5 December 31 5.0 2.8