A paper mill produces two types of paper: paper for books and paper for magazines. The profit contributions are $214 for each ton of paper for books and $261 for each ton of paper for magazines. Each ton of paper for books requires two tons of spruce and four tons of fir; each ton of paper for magazines requires two tons of spruce and two tons of fir. The company must supply at least 25,000 tons of paper for books and at least 20,000 tons of paper for magazines a year. The yearly availability of materials is 278,000 tons of spruce and 420,000 tons of fir. The chief executive officer imposes an additional restriction that the amount of paper manufactured for magazines should be no more than a half of the amount of paper manufactured for books. Determine the amount of paper (in tons) for magazines and the amount of paper (in tons) books to maximize the total profit.

You are head of the schwartz family endowment for the arts. you have decided to fund an arts school in the san francisco bay area in perpetuity. every 5 years, you will give the school $ 1 comma 000 comma 000. the first payment will occur 5 years from today. if the interest rate is 5.9 % per year, what is the present value of your gift?

Areal estate agent is considering changing her cell phone plan. there are three plans to choose from, all of which involve a monthly service charge of $20. plan a has a cost of $.42 a minute for daytime calls and $.17 a minute for evening calls. plan b has a charge of $.52 a minute for daytime calls and $.15 a minute for evening calls. plan c has a flat rate of $80 with 275 minutes of calls allowed per month and a charge of $.38 per minute beyond that, day or evening.a. determine the total charge under each plan for this case: 150 minutes of day calls and 70 minutes of evening calls in a month. (do not round intermediate calculations. round your answer to 2 decimal places. omit the "$" sign in your response.)c. if the agent will use the service for daytime calls, over what range of call minutes will each plan be optimal? (round each answer to the nearest whole number.include the indifference point itself in each answer.)d. suppose that the agent expects both daytime and evening calls. at what point (i.e., percentage of total call minutes used for daytime calls) would she be indifferent between plans a and b?

Suppose your rich uncle gave you $50,000, which you plan to use for graduate school. you will make the investment now, you expect to earn an annual return of 6%, and you will make 4 equal annual withdrawals, beginning 1 year from today. under these conditions, how large would each withdrawal be so there would be no funds remaining in the account after the 4th withdraw?