A potential investor is willing to provide $1,500,000 in the first-round financing with the expectation of a 50% annual compound rate of return over the next five years. Founders currently hold 1,000,000 million shares of stock. The venture is expected to produce $500,000 in net income in year 5. A similar firm with an annual net income of $1,500,000 sold shares to the public for $10,000,000. What is the pre-money valuation?

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.]