1. Linear Programming Problem A manufacturer of three models of tote bag must de
ID: 379129 • Letter: 1
Question
1. Linear Programming Problem
A manufacturer of three models of tote bag must determine the production plan for the next quarter.
The specifics for each model are shown in the following table.
Model
Revenue
($ per item)
Cutting
(hours per item)
Sewing
(hours per item)
Packing
(hours per item)
A
$8.75
.10
.15
.20
B
$10.50
.15
.12
.20
C
$11.50
.20
.18
.20
Time available in the three production departments are: Cutting 450 hours, Sewing 550 hours, Packing 450 hours.
Based on market research, the company wants to make at least 300 model A’s, 400 model B’s and 250 model C’s but no more than 1200 of any one model
Costs in each department are: Cutting $11.00 per hour, Sewing $12.50 per hour, Packing $9.25 per hour
Write the Linear Programming formulation for this problem to help determine the best production mix of the three models that will maximize profit.
Model
Revenue
($ per item)
Cutting
(hours per item)
Sewing
(hours per item)
Packing
(hours per item)
A
$8.75
.10
.15
.20
B
$10.50
.15
.12
.20
C
$11.50
.20
.18
.20
Explanation / Answer
LP model
Let A, B, C indicate quantity of each of the three products to make
Profit per unit = Revenue - time used in each dept * cost per hour
Profit per unit of A = 8.75-(.1*11+.15*12.5+.2*9.25) = 3.925
Profit per unit of B = 10.5-(.15*11+.12*12.5+.2*9.25) = 5.5
Profit per unit of C = 11.5-(.2*11+.18*12.5+.2*9.25) = 5.2
Objective: Max 3.925A+5.5B+5.2C
s.t.
.1A+.15B+.2C <= 450 cutting hours
.15A+.12B+.18C <= 550 sewing hours
.2A+.2B+.2C <= 450 packing hour
A, B, C <= 1200
A >= 300
B >= 400
C >= 250
A, B, C >= 0
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