Marginal CM expresses the “added value” (also called “shadow price”) by increasing x
by one unit. This means that the additional price for materials for product A shall not
exceed = limit CM = 35 DKK/unit of A. Since the limit CM is constant, it can - if the
incremental price is < 35 DKK /unit of A - be worthwhile to import materials to increase
production, until the limit of the milling capacity is reached, i.e. for the production that
is calculated in the solution of question 1.
If the additional cost of materials is = 35 DKK/unit of A, then the CM is not increased by
the import of additional materials. This can be illustrated by the fact that the marginal CM
for product type A with this additional cost is = 160 - 35 = 125 DKK/unit. The slope of the
CM line becomes in this case = -125 / 200 = -0.625. The CM line now has the same slope
as the limiting line for the turning capacity. Thus, the CM is not changed now by moving
up or down this limitation.