Use the linear programming procedure to solve the problem below. Natasha's cat, Dancer, will eat both dry food and wet (canned) food. Natasha wants Dancer to eat meals that are nutritious, but would also like to save some money on her cat's food bill. Dancer usually eats wet food. However, the wet food is more expensive. In order to save money, Natasha is trying to decide if she can switch her cat to a diet with some wet and some
dry food, or perhaps all dry food. However, she wants to ensure that the new diet satisfies Dancer's nutritional requirements.

Protein and fat are two important components of a cat's diet. Proteins serve as building blocks for bones and muscles, while fat provides energy and helps with the absorption of vitamins. Dancer needs at least 60 grams of protein per day and at least 12 grams of fat per
day. The wet food provides about 12 grams of protein per serving while the dry food
provides about 24 grams of protein per serving. The wet food contains about 6 grams of fat while dry food contain about 4 grams of fat per serving. The wet food costs 80 cents per serving and the dry food costs 66 cents per serving. How many servings of wet and dry food will Dancer need each day to meet her nutritional requirements while keeping Natasha's pet food bill a minimum?

identify X and Y:

4 inequalities:

graph the inequalities:

Jobs and productivity! how do retail stores rate? one way to answer this question is to examine annual profits per employee. the following data give annual profits per employee (in units of 1 thousand dollars per employee) for companies in retail sales. assume σ ≈ 4.0 thousand dollars. 3.7 6.7 3.6 8.5 7.5 5.9 8.7 6.4 2.6 2.9 8.1 −1.9 11.9 8.2 6.4 4.7 5.5 4.8 3.0 4.3 −6.0 1.5 2.9 4.8 −1.7 9.4 5.5 5.8 4.7 6.2 15.0 4.1 3.7 5.1 4.2 (a) use a calculator or appropriate computer software to find x for the preceding data. (round your answer to two decimal places.) thousand dollars per employee (b) let us say that the preceding data are representative of the entire sector of retail sales companies. find an 80% confidence interval for μ, the average annual profit per employee for retail sales. (round your answers to two decimal places.) lower limit -- thousand dollars upper limit -- thousand dollars (c) let us say that you are the manager of a retail store with a large number of employees. suppose the annual profits are less than 3 thousand dollars per employee. do you think this might be low compared with other retail stores? explain by referring to the confidence interval you computed in part (b). yes. this confidence interval suggests that the profits per employee are less than those of other retail stores. no. this confidence interval suggests that the profits per employee do not differ from those of other retail stores. correct: your answer is correct. (d) suppose the annual profits are more than 6.5 thousand dollars per employee. as store manager, would you feel somewhat better? explain by referring to the confidence interval you computed in part (b). yes. this confidence interval suggests that the profits per employee are greater than those of other retail stores. no. this confidence interval suggests that the profits per employee do not differ from those of other retail stores. (e) find an 95% confidence interval for μ, the average annual profit per employee for retail sales. (round your answers to two decimal places.) lower limit 3.75 incorrect: your answer is incorrect. thousand dollars upper limit 6.41 incorrect: your answer is incorrect. thousand dollars