=2.18. Nutri-Jenny is a weight-management center. It produces a wide variety of frozen entrees for consumption by its clients. The entrees are strictly monitored for nutritional content to ensure that the clients are eating a balanced diet. One new entree will be a “beef sirloin tips dinner.” It will consist of beef tips and gravy, plus some combination of peas, carrots, and a dinner roll. Nutri-Jenny would like to determine what quantity of each item to include in the entree to meet the nutritional requirements, while costing as little as possible. The nutritional information for each item and its cost are given in the following table.

Calories Calories from Fat Vitamin A Vitamin C Protein Cost Item (per oz.) (per oz.) (IU per oz.) (mg per oz.) (gr. per oz.) (per oz.)
Beef tips 54 19 0 0 8 40¢
Gravy 20 15 0 1 0 35¢
Peas 15 0 15 3 1 15¢
Carrots 8 0 350 1 1 18¢
Dinner roll 40 10 0 0 1 10¢

The nutritional requirements for the entree are as follows:
(1) it must have between 280 and 320 calories, (2) calories from fat should be no more than 30 percent of the total number of calories, and (3) it must have at least 600 IUs of vitamin A, 10 milligrams of vitamin C, and 30 grams of protein. Furthermore, for practical reasons, it must include at least 2 ounces of beef, and it must have at least half an ounce of gravy per ounce of beef.