Question #3 Park Stable feeds and houses the horses used to pull tourist-filled carriages through the streets of Charlestons historic waterfront area. The stable owner, an ex-racehorse trainer, recognizes the need to set a nutritional diet for the horses in his care. At the same time, he would like to keep the overall daily cost of feed to a minimum.

The feed mixes available for the horses diet are an oat product, a highly enriched grain, and a mineral product. Each of these mixes contains a certain amount of five ingredients needed daily to keep the average horse healthy. The following table shows these minimum requirements, units of each ingredient per pound of feed mix, and costs for the three mixes.

In addition, the stable owner is aware that an overfed horse is a sluggish worker. Consequently, he determines that 5 pounds of feed per day are the most that any horse needs to function properly. Formulate this problem and solve for the optimal daily mix of the three feeds.

Question #4 Eddie Kelly is running for reelection as mayor of a small town in Alabama. Jessica Martinez, Kellys campaign manager during this election, is planning the marketing campaign, and there is some stiff competition. Martinez has selected four ways to advertise: television ads, radio ads, billboards, and newspaper ads. The costs of these, the audience reached by each type of ad, and the maximum number available is shown in the following table:

In addition, Martinez has decided that there should be at least 7 ads on TV or radio or some combination of those two. The amount spent on billboards and newspapers together must not exceed the amount spent on TV ads. While fundraising is still continuing, the monthly budget for advertising has been set at $23,000. How many ads of each type should be placed to maximize the total number of people reached?

Question #5 Dr. Pierce wishes to invest his retirement fund of $1,800,000 so that his return on investment is maximized, but he also wishes to keep the risk level relatively low. He has decided to invest his money in any of three possible ways: CDs that pay a guaranteed 2.5 percent; stocks that have an expected return of 10 percent; and a money market mutual fund that is expected to return 15 percent. He has decided that the total $1,800,000 will be invested, but any part (or all) of it may be put in any of the three alternatives. Thus, he may have some money invested in all three alternatives. He has also decided to invest, at most, 30 percent of this in stocks and at least 20 percent of this in money market funds. Formulate this as a linear programming problem and carefully define all the decision variables.