A stock had annual returns of 5.1 percent, 12.2 percent, −3.8 percent, and 9.4 percent for the past four years. The arithmetic average of these returns is percent while the geometric average return for the period is percent.

Apharmaceutical packaging company (ppc) has decided to reorganize its processes into cells. the company has four different production operations, each requiring a unique piece of equipment. the names and functions of the four pieces of equipment are sort, count, place, and package. the company packages five different families of products (a, b, c, d, and e). the tables below indicate the demand (total units/day by product family), required operations, and operation cycle times for each product family. assume that any individual piece of equipment is available to operate 16 hours/day, but 2 hours (in total) are lost each day on each piece of equipment due to breaks and meetings when operators are not available to operate the equipment. how many minutes/day are available for production

Oz makes lion food out of giraffe and gazelle meat. giraffe meat has 18 grams of protein and 36 grams of fat per pound, while gazelle meat has 36 grams of protein and 18 grams of fat per pound. a batch of lion food must contain at least "46,800" grams of protein and 70,200 grams of fat. giraffe meat costs $1/pound and gazelle meat costs $2/pound. how many pounds of each should go into each batch of lion food in order to minimize costs? hint [see example 2.]

You are the manager of a large crude-oil refinery. as part of the refining process, a certain heat exchanger (operated at high temperatures and with abrasive material flowing through it) must be replaced every year. the replacement and downtime cost in the first year is $165 comma 000. this cost is expected to increase due to inflation at a rate of 7% per year for six years (i.e. until the eoy 7), at which time this particular heat exchanger will no longer be needed. if the company's cost of capital is 15% per year, how much could you afford to spend for a higher quality heat exchanger so that these annual replacement and downtime costs could be eliminated?