solve in r programming

2. Investment Strategy An investor has $40,000 to invest. She is considering investments in savings at 7% annual return, municipal bonds at 9% annual return, and stocks that have been averaging 14% annual return. Because there are varying degrees of risk involved in the various investments, the investor has listed the following goals for her portfolio: Have an investment of at least $10,000 in stocks. The investment in stocks should not exceed the combined total in bonds and savings. Have a savings account of no more than $10,000, but no less than $5000. The total investment must not exceed $40,000. The goal of the investor is to maximize her annual dollar return. Hint: The objective function is the annual dollar return, defined as: P = 0.073 +0.09.9 +0.1day, where *) is the savings amount, 12 is the bond investment and #3 is the amount invested in stocks. 2.1 (10pts) Define in R a vector obj with the coefficients of the linear objective function. 2.2 (10pts) Construct in R the 5 x 3 constraint matrix mat, based on the above 5 constraint inequalitics. . 2.3 (10pts) Define in R the direction vector dir with the consraint inequalities. 2.4 (10pts) Define in R the right-hand side vector rhs of the constraints. 2.5 (10pts) Call the lp solver from the IpSolve package to maximize the objective function, given all constraints. What are the optimal investments in the three assets and the maximum dollar return? 2. Investment Strategy An investor has $40,000 to invest. She is considering investments in savings at 7% annual return, municipal bonds at 9% annual return, and stocks that have been averaging 14% annual return. Because there are varying degrees of risk involved in the various investments, the investor has listed the following goals for her portfolio: Have an investment of at least $10,000 in stocks. The investment in stocks should not exceed the combined total in bonds and savings. Have a savings account of no more than $10,000, but no less than $5000. The total investment must not exceed $40,000. The goal of the investor is to maximize her annual dollar return. Hint: The objective function is the annual dollar return, defined as: P = 0.073 +0.09.9 +0.1day, where *) is the savings amount, 12 is the bond investment and #3 is the amount invested in stocks. 2.1 (10pts) Define in R a vector obj with the coefficients of the linear objective function. 2.2 (10pts) Construct in R the 5 x 3 constraint matrix mat, based on the above 5 constraint inequalitics. . 2.3 (10pts) Define in R the direction vector dir with the consraint inequalities. 2.4 (10pts) Define in R the right-hand side vector rhs of the constraints. 2.5 (10pts) Call the lp solver from the IpSolve package to maximize the objective function, given all constraints. What are the optimal investments in the three assets and the maximum dollar return