Optimization

Correction!!

Hint: In each periodt= 1, . . . , T, we have constraints cash inflow = cash outflow

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A company will face the following cash requirements in the next eight quarters (positive entries represent cash needs while negative entries represent cash surpluses). Q1 100 Q2 500 Q3 100 Q4 -600 Q5 -500 Q6 200 Q7 600 Q8 -900 The company has the following products available: A 2-year, i.e. 8 quarter, loan available only at the beginning of Q1, with a 1% interest per quarter, compounded quarterly. This loan has to be repaid at the beginning of Q9. A 6-month, i.e. 2 quarter, loan with 1.8% interest per quarter, compounded quarterly. Available at the beginning of Q1, ..., Q7. A quarterly loan with a 2.5% interest for the quarter. Available at the beginning of Qi, Q8. Any surplus can be invested at a 0.5% interest per quarter. Formulate a linear program that maximizes the wealth of the company at the beginning of Q9. Hint: In each period t = 1,...,T, we have constraints cash inflow - cash outflow. Let 2 qt > 0: amount borrowed using quarterly loan with interest rate ra = 2.5%, t = 1, ...,T 1. St > 0: amount borrowed using six-month loan with interest rate rs = 1.8%, t= 1, ...,T 2. li > 0: amount borrowed using the long-term loan in quarter 1 with interest rate ri = 1%. zt > 0: excess cash available in period t = 1,...,T. A company will face the following cash requirements in the next eight quarters (positive entries represent cash needs while negative entries represent cash surpluses). Q1 100 Q2 500 Q3 100 Q4 -600 Q5 -500 Q6 200 Q7 600 Q8 -900 The company has the following products available: A 2-year, i.e. 8 quarter, loan available only at the beginning of Q1, with a 1% interest per quarter, compounded quarterly. This loan has to be repaid at the beginning of Q9. A 6-month, i.e. 2 quarter, loan with 1.8% interest per quarter, compounded quarterly. Available at the beginning of Q1, ..., Q7. A quarterly loan with a 2.5% interest for the quarter. Available at the beginning of Qi, Q8. Any surplus can be invested at a 0.5% interest per quarter. Formulate a linear program that maximizes the wealth of the company at the beginning of Q9. Hint: In each period t = 1,...,T, we have constraints cash inflow - cash outflow. Let 2 qt > 0: amount borrowed using quarterly loan with interest rate ra = 2.5%, t = 1, ...,T 1. St > 0: amount borrowed using six-month loan with interest rate rs = 1.8%, t= 1, ...,T 2. li > 0: amount borrowed using the long-term loan in quarter 1 with interest rate ri = 1%. zt > 0: excess cash available in period t = 1,...,T