You will receive 27 annual payments of $22,500. The first payment will be received 7 years from today and the interest rate is 5.1 percent. What is the value of the payments today?

Afinancial institution, the thriftem bank, is in the process of formulating its loan policy for the next quarter. a total of $12 million is allocated for that purpose. being a full-service facility, the bank is obligated to grant loans to different clientele. the following table provides the types of loans, the interest rate charged by the bank, and the possibility of bad debt as estimated from past experience.type of loaninterest rateprobability of bad debtpersonal.140.10car.130.07home.120.03farm.125.05commercial.100.02 bad debts are assumed unrecoverable and hence produce no interest revenue either. competition with other financial institutions in the area requires that the bank allocate at least 40% of the total funds to farm and commercial loans. to assist the housing industry in the region, home loans must equal at least 50% of the personal, car, and home loans. the bank also has a stated policy specifying that the overall ratio for bad debts on all loans may not exceed .04. formulate this problem as a linear program. define your variables clearly and write all the constraints explaining the significance of each.

University hero is considering expanding operations beyond its healthy sandwiches. jim axelrod, vice president of marketing, would like to add a line of smoothies with a similar health emphasis. each smoothie would include two free health supplements such as vitamins, antioxidants, and protein. jim believes smoothie sales should fill the slow mid-afternoon period. adding the line of smoothies would require purchasing additional freezer space, machinery, and equipment. jim provides the following projections of net sales, net income, and average total assets in support of his proposal. sandwichesonly sandwiches and smoothies net sales $ 750,000 $ 1,350,000 net income 120,000 210,000 average total assets 350,000 750,000 return on assetschoose numerator ÷ choose denominator = return on assets÷ = return on assets÷ = profit margin÷ = profit margin÷ = asset turnover÷ = asset turnover÷ = times

(30 total points) suppose a firm’s production function is given by q = l1/2*k1/2. the marginal product of labor and the marginal product of capital are given by: mpl = 1/ 2 1/ 2 2l k , and mpk = 1/ 2 1/ 2 2k l . a) (12 points) if the price of labor is w = 48, and the price of capital is r = 12, how much labor and capital should the firm hire in order to minimize the cost of production if the firm wants to produce output q = 18?