A pension fund manager decides to invest a total of at most $30 million in U. S. Treasury bonds paying 4% annual interest and in mutual funds paying 6% annual interest. He plans to invest at least $5 million in bonds and at least $15 million in mutual funds. Bonds have an initial fee of $100 per million dollars, while the fee for mutual funds is $200 per million. The fund manager is allowed to spend no more than $5000 on fees. How much should be invested in each to maximize annual interest? What is the maximum annual interest? The amount that should be invested in Treasury bonds is $nothing million and the amount that should be invested in mutual funds is $nothing million. The maximum annual interest is $nothing.

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.1 20.03farm.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.

In each of the following, what happens to the unemployment rate? does the unemployment rate give an accurate impression of what’s happening in the labor market? a. esther lost her job and begins looking for a new one. b.sam, a steelworker who has been out of work since his mill closed last year, becomes discouraged and gives up looking for work. c.dan, the sole earner in his family of 5, just lost his $90,000 job as a research scientist. immediately, he takes a part-time job at starbucks until he can find another job in his field.

Sales at a fast-food restaurant average $6,000 per day. the restaurant decided to introduce an advertising campaign to increase daily sales. to determine the effectiveness of the advertising campaign, a sample of 49 days of sales were taken. they found that the average daily sales were $6,300 per day. from past history, the restaurant knew that its population standard deviation is about $1,000. if the level of significance is 0.01, have sales increased as a result of the advertising campaign? multiple choicea)fail to reject the null hypothesis. b)reject the null hypothesis and conclude the mean is higher than $6,000 per day. c)reject the null hypothesis and conclude the mean is lower than $6,000 per day. d)reject the null hypothesis and conclude that the mean is equal to $6,000 per day. expert answer