Question

Contract A costs a flat fee of 480 dollars for 90 meals or less

Contract B cost 200 dollars per month plus 4 dollars per meal
Contract C cost a straight 8 dollars per meal
1. What are the domains for the given three contracts?
2. If you expect to eat only 56 of the available meals in a month which contract would be best for you?
3. When might you prefer A?B?C?
4. Write the best choice as a piecewise defined function.

Answer 1

The domains for the three contracts are: 0 ≤ x ≤ 90 for contract A, x ≥ 0 for contract B and contract C. If you expect to eat only 56 meals, contract B would be the best for you. Contract A would be preferred for a smaller number of meals, Contract B for a larger number of meals, and Contract C for convenience. The best choice as a piecewise defined function is f(x) = 480 if x ≤ 90, 200 + 4x if x > 90.

Step-by-step explanation:

The domains for the three contracts are as follows:

1. Contract A: The domain is 0 ≤ x ≤ 90, where x represents the number of meals.
2. Contract B: There is no limit on the number of meals, so the domain is x ≥ 0, where x represents the number of meals.
3. Contract C: There is no limit on the number of meals, so the domain is x ≥ 0, where x represents the number of meals.

If you expect to eat only 56 of the available meals in a month, Contract B would be the best for you because it has a lower cost per meal than Contract A.

You might prefer Contract A if you expect to eat less than 90 meals in a month, as it has a flat fee and may be more cost-effective for a smaller number of meals. Contract B would be preferred if you expect to eat a larger number of meals, as it has a lower cost per meal. Contract C may be preferred if you prioritize convenience over cost, as it offers a straight $8 per meal without any additional fees.

The best choice as a piecewise defined function can be written as: f(x) = 480 if x ≤ 90, 200 + 4x if x > 90 (where x represents the number of meals).