A patient takes vitamin pills. Each day he must have at least 630 IU of vitamin A, 5 mg of vitamin Upper B 1, and 80 mg of vitamin C. He can choose between pill 1, which contains 150 IU of vitamin A, 1 mg of vitamin Upper B 1, and 10 mg of vitamin C, and pill 2, which contains 90 IU of vitamin A, 1 mg of vitamin Upper B 1, and 40 mg of vitamin C. Pill 1 costs 25cents, and pill 2 costs 50cents. Complete parts a and b below.
In this problem, we need to determine the most cost-effective combination of pills in order to meet the daily vitamin requirements of the patient.
Let's define the variables:
- Let x be the number of pill 1.
- Let y be the number of pill 2.
To solve this problem, we need to set up an objective function and some constraints.
a) Objective Function:
We want to minimize the cost, so the objective function would be:
Cost = 0.25x + 0.50y
b) Constraints:
1. Vitamin A Constraint:
We need at least 630 IU of vitamin A, so the constraint would be:
150x + 90y ≥ 630
2. Vitamin B1 Constraint:
We need at least 5 mg of vitamin B1, so the constraint would be:
1x + 1y ≥ 5
3. Vitamin C Constraint:
We need at least 80 mg of vitamin C, so the constraint would be:
10x + 40y ≥ 80
All variables should also be non-negative:
x ≥ 0
y ≥ 0
Now we can solve this problem using linear programming techniques like the Simplex method or graphical method.