9781118041581

Note that a small change in the contribution ratio has no effect on the optimal

plan as long as the requisite inequality continues to hold. For instance, if the

price cut is to $960 (only 4 percent), the new contribution ratio will be

500/260. Production plan C will continue to be optimal because the second

inequality still will be satisfied. (Of course, with the fall in price, the firm’s profit

will drop; nonetheless, the firm should stick to plan C.) If the contribution of

model E falls below half that of model S, production plan B will become opti-

mal.^6 Finally, if the contribution of E exceeds that of S, producing model E

exclusively will produce the most total contribution. In other words, as pro-

duction of one model becomes relatively less and less profitable, the optimal

plan shifts to increasing amounts of the other model.

720 Chapter 17 Linear Programming

FIGURE 17.4

Production Constraints

with New Contributions

A fall in the unit

contribution of

economy PCs causes

the contribution

contour to steepen

and the optimal mix

of PCs to move from

point C to point B.

600

500

300

400

200

100

Economy Models

0 100 200 300 400 500

Standard Models

A

B

C

D

C = $120,000

(^6) If the slope of the objective function contour happens to be identical to the slope of a given con-
straint, any production point along the constraint is optimal. For instance, if S/E 2, maxi-
mum total contribution is attained at points B and C and any other point along segment BC.
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