Question 1153400: A patient takes vitamin pills. Each day he must have at least 150 IU of vitamin A, 3 mg of vitamin Upper B 1, and 30 mg of vitamin C. He can choose between pill 1, which contains 90 IU of vitamin A, 1 mg of vitamin Upper B 1, and 5 mg of vitamin C, and pill 2, which contains 30 IU of vitamin A, 1 mg of vitamin Upper B 1, and 20 mg of vitamin C. Pill 1 costs 25cents, and pill 2 costs 75cents. How many of Pill 1 and pill 2 should he buy? What is the minimum cost?
Answer by ikleyn(52770)   (Show Source):
You can put this solution on YOUR website! .
The need vitamin A Vitamin B1 Vitamin C
150 IU 3 mg 30 mg
Pill 1 90 IU 1 mg 5 mg
Pill 2 30 IU 1 mg 20 mg
There are not so many configurations n*Pill1 + m*Pill2, so we can easily analyse all potential variants.
Cost, in cents
1*Pill1+2*Pill2 150 IU 3 mg 45 mg 175
6*Pill1+0*Pill2 540 IU 6 mg 30 mg 150
0*Pill1+5*Pill2 150IU 5 mg 100 mg 375
All other variants EITHER do not provide the required parameters OR are farther from the goal, regarding the price, obviously.
So, there are only these 3 variants, of them variant 6 Pills 1 + 0 Pills 2 is the most cheaper.
ANSWER. Version (6 Pills 1 + 0 Pills 2) provides the required parameters and is the most cheap. It costs $1.50.
Solved.
|
|
|
