a.
Formulate the problem in terms of linear inequalities and an objective
function.
b.
Solve the problem geometrically.
c.
Explain how the 2:1 cost ratio (steak to potatoes) dictates that the solution
must be where you said it is.
d.
Find a cost ratio that would move the optimal solution to a different choice of
numbers of food units, but that would still require buying both steak and
potatoes.
e.
Find a cost ratio that would dictate buying only one of the two foods in order
to minimize cost.
We begin by setting the constraints for the problem. The first constraint
represents the minimum requirement for carbohydrates, which is 8 units per some
unknown amount of time. 3 units can be consumed per unit of potatoes and 1 unit
can be consumed per unit of steak. The second constraint represents the minimum
requirement for vitamins, which is 19 units. 4 units can be consumed per unit
of potatoes and 3 units can be consumed per unit of steak. The third constraint
represents the minimum requirement for proteins, which is 7 units. 1 unit can
be consumed per unit of potatoes and 3 units can be consumed per unit of steak.
The fourth and fifth constraints represent the fact that all feasible solutions
must be nonnegative because we can t buy negative quantities.