Herbes de Provence produces jams, jellies and oils using their home-grown herbs. They are planning to expand their product line to include soaps, shampoos, lotions, and other personal care products featuring their herbs. Construction of the new facility will cost $450,00. The end-of-month payment schedule is provided below along with the different start-of-month investment options for creating a sinking fund to meet the payments.

Formulate an LP to meet the required schedule while placing the least amount of money into the sinking fund. Do NOT solve.

Payment schedule: End of month: 1 2 3 Amount due (S1000s) $150 $0 $100 4 5 $0 $75 6 7 $75 $50 Investments available: Investment A B D E Available start of month: Months to Maturity Yield at Maturity (end of month) 1 7 10.5% 1,3 6.1% 1,4 4 5.5 % 1, 3,5 3 4.7 % 1, 2, 3, 4, 5, 6, 7 3.6 % 5 1 Payment schedule: End of month: 1 2 3 Amount due (S1000s) $150 $0 $100 4 5 $0 $75 6 7 $75 $50 Investments available: Investment A B D E Available start of month: Months to Maturity Yield at Maturity (end of month) 1 7 10.5% 1,3 6.1% 1,4 4 5.5 % 1, 3,5 3 4.7 % 1, 2, 3, 4, 5, 6, 7 3.6 % 5 1