Question

A patient takes vitamin pills. Each day he must have at least 420 IU of vitamin A, 5 mg of vitamin

B1, and 60 mg of vitamin C. He can choose between pill 1, which contains 120 IU of vitamin A, 1
mg of vitamin B1, and 10 mg of vitamin C, and pill 2, which contains 60 IU of vitamin A, 1 mg of
vitamin B7, and 15 mg of vitamin C. Pill 1 costs 30¢, and pill 2 costs 60¢. Complete parts a and b
below.

Answer 1

minimum cost is 70 cents when Greg buys 3 pill type 1, and 2 pills type 2.

Explanation:

Answer 2

Pill 1 is more cost-effective, meeting or exceeding daily requirements for vitamins A, B1, and C with lower cost (30¢) compared to pill 2 (60¢). It provides 480 IU of vitamin A, 5 mg of vitamin B1, and 60 mg of vitamin C with fewer pills, making it the optimal choice.

Explanation:

The patient's daily requirements are 420 IU of vitamin A, 5 mg of vitamin B1, and 60 mg of vitamin C. Let's evaluate the contribution of each pill to these requirements.

Pill 1 provides 120 IU of vitamin A, 1 mg of vitamin B1, and 10 mg of vitamin C.

Pill 2 provides 60 IU of vitamin A, 1 mg of vitamin B7, and 15 mg of vitamin C.

To meet the vitamin A requirement, the patient can take 4 pills of type 1 (4 * 120 IU = 480 IU), while it would take 7 pills of type 2 (7 * 60 IU = 420 IU). So, pill 1 is more efficient for meeting the vitamin A requirement.

For vitamin B1, both pills contribute 1 mg each, and since the requirement is 5 mg, the patient needs to take 5 pills of either type.

For vitamin C, the patient needs 60 mg. Pill 1 provides 10 mg per pill, so 6 pills are needed (6 * 10 mg = 60 mg). Pill 2 provides 15 mg per pill, so 4 pills are needed (4 * 15 mg = 60 mg).

Considering the cost, pill 1 costs 30¢, and pill 2 costs 60¢. Since both pills are equally effective in meeting the B1 requirement and pill 1 is more efficient for vitamin A and equally efficient for vitamin C, the patient should choose pill 1 due to its lower cost.