Paige Rufolo recently won a lottery with a prize amount of $750,000 and she wants to invest it so that she maximizes cash at the end of four years. Leftover cash Khat is not invested may be carried over from one year to the next, with no risk. She has the following investments to consider: Fund Available Return at maturity Matures in Risk index Every year 14% 2 years 3 Y Every year 10% 2 z Year 2 24% 3 years 5 1 year Paige has to pay a court settlement of $85,000 at the end of three years. She prefers a portfolio risk no more than 4 in any year. The decision variables have been defined for you: Xi = # of dollars invested in fund X at the beginning of year i, where i = 1, 2, 3 Y = # of dollars invested in fund Y at the beginning of year , where j = 1, 2, 3, 4 Z2 = # of dollars invested in fund Z at the beginning of year 2 G= uninvested (left over) cash at the beginning of year ), where j = 1, 2, 3, 4 Formulate the requested parts of the LP model using the decision variables defined. No grade if you make up your own variables OR if you write out the entire model! 1. Write the objective function. Do not simplify. 2. Write the constraint for the beginning of year 2. Do not simplify. 3. Write the constraint for the beginning of year 4. Do not simplify. 4. Write the risk constraint for year 3. Do not simplify. Paige Rufolo recently won a lottery with a prize amount of $750,000 and she wants to invest it so that she maximizes cash at the end of four years. Leftover cash Khat is not invested may be carried over from one year to the next, with no risk. She has the following investments to consider: Fund Available Return at maturity Matures in Risk index Every year 14% 2 years 3 Y Every year 10% 2 z Year 2 24% 3 years 5 1 year Paige has to pay a court settlement of $85,000 at the end of three years. She prefers a portfolio risk no more than 4 in any year. The decision variables have been defined for you: Xi = # of dollars invested in fund X at the beginning of year i, where i = 1, 2, 3 Y = # of dollars invested in fund Y at the beginning of year , where j = 1, 2, 3, 4 Z2 = # of dollars invested in fund Z at the beginning of year 2 G= uninvested (left over) cash at the beginning of year ), where j = 1, 2, 3, 4 Formulate the requested parts of the LP model using the decision variables defined. No grade if you make up your own variables OR if you write out the entire model! 1. Write the objective function. Do not simplify. 2. Write the constraint for the beginning of year 2. Do not simplify. 3. Write the constraint for the beginning of year 4. Do not simplify. 4. Write the risk constraint for year 3. Do not simplify