An animal breeder can buy four types of food for Vietnamese pot-bellied pigs. Each case of Brand A contains 35 units of fiber, 40 units of protein, and 40 units of fat. Each case of Brand B contains 70 units of fiber, 50 units of protein, and 30 units of fat. Each case of Brand C contains 175 units of fiber, 110 units of protein, and 60 units of fat. Each case of Brand D contains 140 units of fiber, 100 units of protein, and 50 units of fat. How many cases of each brand should the breeder mix together to obtain a food that provides 2450 units of fiber, 1630 units of protein, and 930 units of fat? Let x represent the number of cases of Brand A, y represent the number of cases of Brand B, z represent the number of cases of Brand C, and w represent be the number of cases of Brand D. There are four ways in which the breeder can mix brands to obtain a food that provides 2450 units of fiber, 1630 units of protein, and 930 units of fat. If w = 0, the solution is (O.I.I, 0).

Cholesterol Cholesterol in human blood is necessary, but too much can lead to health problems. There are three main types of cholesterol: HDL (high-density lipoproteins), LDL (low-density lipoproteins), and VLDL (very low-density lipoproteins). HDL is considered “good” cholesterol; LDL and VLDL are considered “bad” cholesterol. A standard fasting cholesterol blood test measures total cholesterol, HDL cholesterol, and triglycerides. These numbers are used to estimate LDL and VLDL, which are difficult to measure directly. Your doctor recommends that your combined LDL/VLDL cholesterol level be less than 130 milligrams per deciliter, your HDL cholesterol level be at least 60 milligrams per deciliter, and your total cholesterol level be no more than 200 milligrams per deciliter. (a) Write a system of linear inequalities for the recommended cholesterol levels. Let x represent the HDL cholesterol level, and let y represent the combined LDL VLDL cholesterol level. (b) Graph the system of inequalities from part (a). Label any vertices of the solution region. (c) Is the following set of cholesterol levels within the recommendations? Explain. LDL/VLDL: 120 milligrams per deciliter HDL: 90 milligrams per deciliter Total: 210 milligrams per deciliter (d) Give an example of cholesterol levels in which the LDL/VLDL cholesterol level is too high but the HDL cholesterol level is acceptable. (e) Another recommendation is that the ratio of total cholesterol to HDL cholesterol be less than 4 (that is, less than 4 to 1). Identify a point in the solution region from part (b) that meets this recommendation, and explain why it meets the recommendation.

1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.6. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.6 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 1 Food C 1 1 2

8.5.17 Kyle works at a donut factory, where a 10-oz cup of coffee costs 95¢, a 14-oz cup costs $1.15, and a 20-oz cup costs $150. During one busy period, Kyle served 28 cups of coffee, using 424 ounces of coffee, while collecting a total of $34.40. How many cups of each size did Kyle fill? Kyle filled 10-oz cup(s). 14-oz cup(s), and 20-oz cup(s). orrec ess Library Enter your answer in the edit fields and then click Check Answer. Check Answer Clear All