she would like to do is to go home and analyse the problem with a pencil and
paper.
Linear programming problemsTanya’s always been coached to visualize
her goals. If she can apply this to winning Olympic gold, why not to
mathematics? So she draws a picture of the feasible region. This is possible
because she is only considering two foods. The line AD represents the
combinations of Solido and Liquex that contain exactly 120 mg vitamins. The
combinations above this line have more than 120 mg vitamins. The line EC
represents the combinations that contain exactly 880 mg minerals. The
combinations of foods that are above both these lines is the feasible region and
represents all the feasible combinations Tanya could buy.
Problems with the framework of the diet problem are called linear
programming problems. The word ‘programming’ means a procedure (its usage
before it became synonymous with computers) while ‘linear’ refers to the use of
straight lines. To solve Tanya’s problem with linear programming,
mathematicians have shown that all we need to do is to work out the size of the
food bill at the corner points on Tanya’s graph. Tanya has discovered a new
feasible solution at the point B with coordinates (48, 8) which means that she
could purchase 48 packets of Solido and 8 cartons of Liquex. If she did this she
would satisfy her diet exactly because in this combination there is 120 mg of
vitamins and 880 mg of minerals. At £5 for both a packet and a carton this
combination would cost her £280. So the optimum purchase will remain as it