increase its profit by switching a second unit (by exactly the same logic). It can
continue to increase its profit by moving along segment DC until it attains the
production plan corresponding to point C. Here, it can no longer improve its
profit because it runs up against the hard-disk capacity constraint. Having
exploited all its options for increasing its profit, the firm has arrived at its opti-
mal product mix.^3
What are the precise model quantities at point C? Since point C lies on the
constraint lines corresponding to hard disks and labor, we know that these con-
straints are binding; that is, the optimal mix uses up all available hard-disk
capacity and labor. Thus, S and E satisfy the constraints, 80S 40E 20,000
and 5S 5E 2,000. Solving these two equations in two unknowns, we find
that S 100 and E 300. Total contribution is (500)(100) (300)(300)
$140,000 after inserting the optimal quantities into the objective function.714 Chapter 17 Linear Programming(^3) Check for yourself that, starting from point B, the firm also profits by moving toward point C.
How much does contribution increase if it produces an extra economy unit?
600
500
300
400
200
100
0
Economy Models
0 100 200 300 400 500
Standard Models
A
B
C
D
= $200,000
= $120,000
= $75,000
= $140,000
FIGURE 17.2
Production Constraints
with Contribution
Contours
The firm’s profit-
maximizing
combination of
computers occurs at
point C, where the
highest contribution
contour touches the
feasible region.
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