You plan to retire at age 65, and you want to have enough money in your savings account to withdraw $54,000 every year for 20 years after that. your account earns 9% interest per year. if you're currently 30, how much money do you need to put in the account each year until you're 65 (35 years) to make that happen? (note: you put in the last deposit in one year and make the first withdrawal in the next. there is no gap.)

Imagine us is a startup that offers high definition 3d prenatal ultrasounds for high-end customers. the service process includes four activities that are conducted in the sequence described below. (the time required for each activity is shown in parentheses): activity 1: welcome a patient and explain the procedure. (20 minutes)activity 2: prep the patient (e.g., show them to the room, apply ultrasound gel). (17 minutes) (*your id number represents the amount of time needed to complete this task)activity 3: take images. (5 minutes)activity 4: discuss diagnostic with patient. (20 minutes)at each location there are employees (servers) s1, s2, and s3. the assignment of tasks to servers is the following: s1 does activities 1 and 2.s2 does activity 3.s3 does activity 4.a. what is the capacity of this process (in customers per hour)? b. suppose 3 patients arrive every hour on average. ignoring any “start of day” or “end of day” effects, what are the utilizations of all three servers (%)? c. suppose each activity can be done by any server and any server can do any set of activities. however, each activity is done by only one server. for example, a possible assignment includes: s1 does activity 1, s2 does activity 2, and s3 does activities 3 and 4. of course, the original assignment of servers to activities is also feasible. what is the maximum capacity of the process (in customers per hour)? d. now consider the capacity measures in (c) and (a), what is the percentage change? why can you improve capacity without using additional resources? (there is no free lunch, right? )note: for all hw assignments, show your process of getting the results. only providing the final answers is not acceptable and will get 0%. if necessary, use a separate sheet of paper to show your work.

In a recent annual report, apple computer reported the following in one of its disclosure notes: "warranty expense: the company provides currently for the estimated cost for product warranties at the time the related revenue is recognized." this note exemplifies apple's use of: (a) conservatism.(b) matching. (c) realization principle. (d) economic entity.

Upper a fish farm raises salmon and trout.a fish farm raises salmon and trout. the marginal cost of producing each of these products increases as more is produced. draw the firm's ppf. label it ppf1. the fish farmfish farm adopts a new technology that allows it to use fewer resources to feed the salmonfeed the salmon. draw a ppf that shows the impact of the new technology. label it ppf2.