Exercise $3\mathrm{.}4$ A company will face the following cash requirements in the

next eight quarters $($positive entries represent cash needs while negative entries

represent cash surpluses$)$:

The company has three borrowing possibilities.

A $2-$year loan available at the beginning of Q$1,$ with a $1\%$ interest per quarter.

The other two borrowing opportunities are available at the beginning of every

quarter: a $6-$month loan with a $1\mathrm{.}8\%$ interest per quarter, and a quarterly

loan with a $2\mathrm{.}5\%$ interest for the quarter.

Any surplus can be invested at a $0\mathrm{.}5\%$ interest per quarter.

Formulate a linear program that maximizes the wealth of the company at the

beginning of Q$9.$