Key to High Step Shoes
Step 1
A = # of Airheads
G = # of Groundeds
Profit = 10A + 8.5 G
Step 3 (continued)
Feasible Region is ABCD.
x-axis represents # of Airheads
y-axis represents # of Groundeds
Step 2
hr .
min.
6 × 50 min.
hr . × 40 wk . = 12, 000 wk .
Step 4
1. Answers will vary.
Though the number of points with
integer values in the feasible region is
finite, it would be impractical without
a computer to generate and check
them all.
2. Corner pts. Profit
(0, 0)
0
(0, 4250)
$36,125
(2800, 1800) $43,300
(4000, 0)
$40,000
3 A + 2G ≤ 12, 000
1
hr .
hr .
850 × 40 wk
. = 34, 000 wk .
7 A + 8G ≤ 34, 000
2
Yes, they might shut down and produce
nothing, or there might be a great demand
for one kind or a surplus of one so that they
shut a line down.
3
A≥0
4
G≥0
Point with largest profit: (2800,1800)
Maximum profit: $43,300
2800 Airsteps, 1800 Groundeds
Why?
Step 3
1 3 A + 2G ≤ 12, 000
2 7 A + 8G ≤ 34, 000
3 A≥0
4 G≥0
G = -1.18A + 2941.18
G = -1.18A + 3529.41
G = -1.18A + 5094.12
G = -1.18A + 5294.12
G = -1.18A + 5882.35
x-intercept y-intercept
1 (4000, 0)
(0, 6000)
2 (4857.14, 0) (0, 4250)
Slope is -1.18.
Lines are parallel.
Two lines segments fall within the feasible
region,
10A + 8.5G = 25000 and
10A + 8.5 G = 30000,
on interval [0, 4000].
At the corner point that gives the optimal
solution.
Linear Programming
-1-
Mathematics & Science Center 2004