Each Day Larry Needs at Least 10 Units of Vitamin $A$

Each day Larry needs at least 10 units of vitamin A, 12 units of vitamin B, and 20 units of vitamin C. Pill \#1 contains 4 units of $A$ and 3 of B. Pill \#2 contains 1 unit of A, 2 of B, and 4 of C. Pill \#3 contains 10 units of A, 1 of B, and 5 of $C$ .
-Pill #1 costs 4 cents, pill #2 costs 10 cents, and pill #3 costs 1 cent. How many of each pill must Larry take to minimize his cost?

A) $\mathrm{P}_{1}=1, \mathrm{P}_{2}=0, \mathrm{P}_{3}=9$
B) $P_{1}=2, P_{2}=0, P_{3}=6$
C) $\mathrm{P}_{1}=3, \mathrm{P}_{2}=0, \mathrm{P}_{3}=4$
D) $\mathrm{P}_{1}=0, \mathrm{P}_{2}=0, \mathrm{P}_{3}=12$