Question

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.

Answer 1

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