The manager of the school cafeteria is planning a plate lunch. She can spend no more than $2.00 per lunch and can
choose servings from selections A and B. The table indicates the cost and the quantity of sugar and protein (in grams)
per serving of each food choice.
Food Cost per serving Sugar Protein
A 20 cents 7 grams 6 grams
B 40 cents 3 grams 9 grams
It is recommended that the lunch contain at most 30 grams of sugar and at least 50 grams of protein. Note: Fractional
servings of each of the food choices can be prepared.
1. Is it possible to prepare a lunch that contains four servings of Food A and three servings of Food B and still satisfy the
constraints on cost, amount of sugar, and amount of protein? Explain.
2. Let a represent the number of servings of food A and let b represent the number of servings of food B. Write a set of
inequalities that model the constraints on cost, amount of sugar, and amount of protein.
1 answer