Please solve these three problems.The task consists of writing a repair formula by hand and solving it using an accelerator.

Problem 1 ( 30 points). Yonsei Bank issues five types of loans. In addition, to diversify its portfolio, and to minimize risk, Yonsei invests in risk-free securities. The loans and the risk-free securities with their annual rate of return are given in the following table. Yonsei's objective is to maximize the annual rate of return on investments subject to the following policies, restrictions, and regulations. 1. Yonsei has $90 million in available funds. 2. Risk-free securities must contain at least 10 percent of the total funds available for investments. 3. Home improvement loans cannot exceed $8,000,000. 4. The investment in home mortgage loans must be at least 60 percent of all the funds invested in loans. 5. The investment in home mortgage loans A must be at least twice as much as the investment in home mortgage loans B. 6. Home improvement loans cannot exceed 40 percent of the funds invested in home mortgage loans A. 7. Automobile loans and home improvement loans together may not exceed the commercial loans. 8. Commercial loans cannot exceed 50 percent of the total funds invested in home mortgage loans. Formulate an algebraic model for this LP problem (define the decision variables, identify the objective function and each of constraints, and provide a model in a complete form). Problem 2. [Please do not use Excel model and Solver!] Consider the following linear program: Maxz=3x+2ys.t.x+y10(C1)3x+y24(C2)x+2y16(C3)andx0,y0 A. Use the graphical solution procedure to find the optimal solution. B. Assume that the objective function coefficient for x changes from 3 to 5 . Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. C. Find the allowable range of the coefficient for x and y. D. Assume that the objective function coefficient for x changes from 3 to 5 and the coefficient for y changes from 2 to 4 . Does the optimal solution change? Problem 3. The production manager for the Yonsei Corporation must determine how many units of product to produce over the next four months. Yonsei has a beginning inventory of 100 units, and demand for the four months is 2000 units in month 1, 4000 units in month2, 3000 units in month 3 , and 1500 units in month 4. Yonsei has limited production capacity in each month. That is, up to 4000 units can be produced in month 1, 3000 units in month 2, 2000 units in month 3, and 4000 units in month 4. Each product held in inventory in months 1 and 2 incurs an inventory holding cost of $250 per unit; the holding cost for months 3 and 4 is $300 per unit. The production costs for the first month are $10,000 per unit; these costs expected to increase by 10% each month because of increases in labor and material costs. Yonsei specified that the ending inventory for month 4 must be at least 500 units. A. Formulate a spreadsheet model that can be used to determine the production schedule that will minimize the total cost of meeting demand in each month. B. Using the sensitivity report, answer the following questions: - What is the optimal solution and what is the optimal value of the objective function? - What is the maximum inventory holding cost for month 3 for which the original optimal solution remains optimal. Interpret your answer. - If Yonsei does not have any beginning inventory, how much would this change the objective function value? Answer this question without recalculation and justify your answer. - If Yonsei can produce up to 4100 units in month 1, how much would this change the objective function value? Answer this question without recalculation and justify your