Math 40
Linear Programming Example
Seall Manufacturing Company makes television sets. It produces a bargain set that sells for $100
profit and a deluxe set that sells for $150 profit. On the assembly line the bargain set requires 3
hours, and the deluxe set takes 5 hours. The cabinet shop spends 1 hour on the cabinet for the
bargain set and 3 hours on the cabinet for the deluxe set. Both sets require 2 hours of time for
testing and packing. On a particular run, the Seall Company has available 3900 work-hours on the
assembly line, 2100 work-hours in the cabinet shop, and 2200 work-hours in the testing and packing
department. How many sets of each type should it produce to make a maximum profit? What is
the maximum profit?
bargain sets
deluxe sets
total
how many
x
y
profit ($)
100
150
assembly line (hrs)
3
5
≤ 3900
cabinet shop (hrs)
1
3
≤ 2100
testing and packing (hrs)
2
2
≤ 2200
Maximize
subject to
z = 100x + 150y
3x + 5y ≤ 3900
x + 3y ≤ 2100
2x + 2y ≤ 2200
x ≥ 0, y ≥ 0
=⇒ x + y ≤ 1100
x
0
300
800
1100
12
10
x + y = 1100
8
(0, 700)
6
y
700
600
300
0
z = 100x + 150y
105,000
120,000
125,000⇐=
110,000
(300, 600)
x + 3y = 2100
4
(800, 300)
2
3x + 5y = 3900
2
4
6
8
(1100, 0)
10
12
14
16
18
20
22
Produce 800 bargain sets and 300 deluxe sets for a maximum profit of $125,000.