cartons. Surely this will be OK? She recalculates and finds she has 2 × 40 + 3 ×
15 = 125 mg vitamins and 10 × 40 + 50 × 15 = 1150 mg minerals. Now Tanya
certainly satisfies her coach’s recommendation and has even exceeded the
required amounts.
Feasible solutions
The combination (40, 15) of foods will enable Tanya to satisfy the diet. This is
called a possible combination, or a ‘feasible’ solution. We have seen already that
(30, 5) is not a feasible solution so there is a demarcation between the two types
of combinations – feasible solutions in which the diet is fulfilled and non-feasible
solutions in which it is not.
Tanya has many more options. She could fill her trolley with only Solido. If
she did this she would need to buy at least 88 packets. The purchase (88, 0)
satisfies both requirements, because this combination would contain 2 × 88 + 3
× 0 = 176 mg vitamins and 10 × 88 + 50 × 0 = 880 mg minerals. If she
bought only Liquex she would need at least 40 cartons, the feasible solution (0,
40) satisfies both vitamin and mineral requirements, because 2 × 0 + 3 × 40 =
120 mg vitamins and 10 × 0 + 50 × 40 = 2000 mg minerals. We may notice
that the intake of vitamins and minerals is not met exactly with any of these
possible combinations though the coach will certainly be satisfied Tanya is having
enough.
Optimum solutions
Money is now brought into the situation. When Tanya gets to the checkout she
must pay for the purchases. She notes that the packets and cartons are equally
priced at £5 each. Of the feasible combinations we have found so far (40, 15),
(88, 0) and (0, 40) the bills would be £275, £440 and £200, respectively so the
best solution so far will be to buy no Solido and 40 cartons of Liquex. This will
be the least cost purchase and the dietary requirement will be achieved. But how
much food to buy has been hit and miss. On the spur of the moment Tanya has
tried various combinations of Solido and Liquex and figured out the cost in these
cases only. Can she do better? Is there a possible combination of Solido and
Liquex that will satisfy her coach and at the same time cost her the least? What