9781118041581

40  20 60 labor-hours. This pair of inputs occurs at point D in Figure 17.6,

halfway along the segment joining A and B. In general, by using processes 1 and

2 in various proportions to produce 40 units in total, we trace out the line seg-

ment AB. Similarly, combinations of processes 2 and 3 use inputs described by

the line segment BC.

To complete the graphical solution, we find the highest production con-

tour attainable given the fixed supply of inputs. The highest contour touches

the corner of the feasible region at point M, where each input is fully uti-

lized. At this point, the firm produces output using only processes 1 and 2.

728 Chapter 17 Linear Programming

Labor-Hours

140

160

100

120

60

80

20

40

0 20 40 60 80 100 120 140 160

Input requirements

for process 1

Optimal corner:

x 1 = 20, x 2 = 50,

Q = 70

LM

K

B

D

A

C

Input requirements

for process 2

Input requirements

for process 3

70-unit

output contour

40-unit

output contour

Machine-Hours

O

FIGURE 17.6

Maximum Output

with Limited Inputs

With 60 machine-hours

and 90 labor-hours,

the firm can produce

its maximum output,

70 units, at point M by

using processes 1 and 2

in combination.

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