Iii Cent
Linear system problem?
A man is ordered by his doctor to take 5 units of vitamin A, 13 units of vitamin B, and 23 units of vitamin C each day. Three brands of vitamin pills are available, and the number of units of each vitamin per pill are shown below:
Vitamin (number of units per pill)
Pill A B C
Brand I 1 2 4
Brand II 1 1 3
Brand III 0 1 1
(i) Let x; y; z denote the number of pills of brand I, II, III respectively. The combinations (x; y; z) that provide the exact required daily amount of vitamins can be solved by a linear system. Write down such a linear system.
(ii) Write down all possible combinations of the number of pills that satisfy the linear system in (i) (no partial pills allowed).
(iii) If brand I costs 3 cents per pill, brand II costs 2 cents per pill, and brand III costs 5 cents per pill, find the least expensive combination in (ii).
require
1x+1y+0z = 5
2x+1y+1z =13
4x+3y+1z = 23
but 2* first + second = third, so third gives no more information
we need
x+y = 5 from first
z-y = 3
so we can have
0,5,8
1,4,7
2,3,6
3,2,5
4,1,4
5,0,3
for cost its easiest just to calculate for each of the six possibilities
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