More general diet problem
Minimum problem has n unknowns, n foods to be eaten in amounts x1,… , xn
m constraints represent m required vitamins
entry aij is amount of i-th vitamin in j-th food.
i-th row of Ax >=b forces the diet to include that vitamin in at least the amount bi.
c1x1 + …. + cnxn = cost of diet (cj is cost of j-th food.)
Dual -- druggist selling vitamin pills rather than food.
Prices adjustable as long as nonnegative.
Key constraint -- on each food can’t charge more than grocer.
Since food j contains vitamins in amount aij , the druggist’s price for the equivalent in vitamins can’t exceed cj => yA <= c.
Can then sell amount bi of each vitamin for a total income of y1b1+..+ ymbm