SOLUTION: 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 c

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(52771) (Show Source): You can put this solution on YOUR website!
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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.

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SOLUTION: 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 c

SOLUTION: 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 c