Adirondack Savings Bank (ASB) has $1 million in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates of return for the three types of loans are 7% for home loans, 11% for personal loans, and 10% for automobile loans. The bank's planning committee has decided that at least 40% of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated to personal loans cannot exceed 60% of the amount allocated to automobile loans. (a) Formulate a linear programming model that can be used to determine the amount of funds ASB should allocate to each type of loan to maximize the total annual return for the new funds. If the constant is "1" it must be entered in the box. If your answer is zero enter "0". Let H = amount allocated to home loans Pe amount allocated to personal loans A = amount allocated to automobile loans Max 0.07 H+ 0.14 P+ 0.11 A sit. H + P + A2 Minimum Home Loans H + P + AS Loan Red ement H+ P+ A Amount of New Funds (b) How much should be allocated to each type of loan? Loan type Allocation Home Personal Automobile What is the total annual return? If required, round your answer to nearest whole dollar amount. S What is the annual percentage return? If required, round your answer to two decimal places. % (c) If the interest rate on home loans increases to 9%, would the amount allocated to each type of loan change? If required, round your answer to nearest whole dollar amount. - Select your answer - What is the annual percentage return? If required, round your answer to two decimal places 96 (c) If the interest rate on home loans increases to 9%, would the amount allocated to each type of loan change? - Select your answer - Explain An increase to 94 - Select your answer within the allowable range, to the amount allocated to each type of loan change. (d) Suppose the total amount of new funds available & increased by $10,000. What effect would this have on the total annual return? Explain. If required, round your answer to nearest whole dollar amount. An increase of $10,000 to the total amount of funds available would increase the total annual return by s (e) Assume that ASB has the original $1 million in new funds available and that the planning committee has agreed to relax the requirement that at least 40% or the new funds must be allocated to home loans by 1%. How much would the annual return change? If required, round your answer to nearest whole dollar amount 5 How much would the annual percentage return change? If required, round your answer to two decimal places % 1132) Industrial Designs has been awarded a contract to design a label for a new wine produced by Lake View Winery. The company estimates that 150 hours will be required to complete the project. The firm's three graphic designers available for assignment to this project are Lisa, a senior designer and team leader; David, oa senior designer; and Sarah, a junior designer. Because Lisa has worked on several projects for Lake View Winery, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers. To provide label designing experience for Sarah, the Junior designer must be assigned at least 15% of the total project time. However, the number of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers. Due to other project commitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $23 for David, and $18 for Sarah. (a) Formulate a linear program that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize total cost. If an amount is zero, enter "0". If the constant is "1" it must be entered in the box. For negative numbers use a minus sign (Example: enter -100). Let L = number of hours assigned to Lisa D number of hours assigned to David S = number of hours assigned to Sarah Min s L+ D+ $ S st D + S 2 Minimum Usa 2 + D + S 2 Minimum Sarah L + D + S s Maximum Lisa + D + + S 5 s Maximum Sarah 2 + D + s Total Time LDS > 0 (b) How many hours should be assigned to each graphic designer? Hours Assigned Lisa David Sarah What is the total cost? If required, round your answer to a whole dollar amount (b) How many hours should be assigned to each graphic designer Hours Assigned David Sarah What is the total cost? If required, round your answer to a whole dollar amount will (C) Suppose Lisa could be assigned more than 50 hours. What effect would this have on the optimal solution? Explain. If an amount is zero, enter "o". We know that the shadow price for this constraint is since the constraint is - Select your answer Therefore, additional hours for Lisa Select your answer the solution, (a) Ir Sarah were not required to work a minimum number of hours on this project, would the optimal solution change? - Select your answer. Explain There - Select your answer v lower limit on the right-hand-side range, so the optimal solution Select your answer change. Check My Work Ooon
