CHAPTER 3
LINEAR PROGRAMMING MODELING APPLICATIONS
WITH COMPUTER ANALYSES IN EXCEL
SOLUTIONS TO PROBLEMS
31.
Let F = number of French Provincial cabinets produced each day, and D = number of Danish Modern
cabinets produced each day
Objective: Maximize revenue = $28F + $25D
Subject to
3F + 2D ≤ 360 hours
(carpentry department)
1½F + 1D ≤ 200 hours
(painting department)
¾F + ¾D ≤ 125 hours
(finishing department)
F ≥ 60 units
(contract requirement)
D ≥ 60 units
(contract requirement)
Solution: See file P31.XLS.
Produce 60 French Provincial cabinets and 90 Danish Modern cabinets per day. Profit = $3,930.
32.
Let C = number of canvas backpacks produced.
P, N, L defined similarly.
Objective: Maximize profit
=
(Canvas revenue – Canvas cost)*C + (Plastic revenue – Plastic cost)*P +
(Nylon revenue – Nylon cost)*N + (Leather revenue – Leather cost)*L
=
Maximize $14.88C + $18.80P + $12.80N + $27.83L
Subject to:
2.25C
200
Canvas available
2.40P
350
Plastic available
2.10N
700
Nylon available
2.60L
550
Leather available
1.5C
+ 1.5P
90
Canvas & Plastic labor
1.7N
42.
5
Nylon labor
1.9 L
80
Leather labor
C,
P,
N,
L
40
Max production
C,
P,
N,
L
15
Min production
Solution: See File P32N.XLS.
Produce 20 Canvas, 40 Plastic, 25 Nylon, and 40 Leather backpacks. Profit = $2,483.58.
33.
Let
I = no. of units of internal modems produced per week
E = no. of units of external modems produced per week
C = no. of units of circuit boards produced per week
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F = no. of units of floppy disk drives produced per week
H = no. of units of hard drives produced per week
M = no. of units of memory boards produced per week
Objective function analysis:
First find the time used on each test device:
Hours on test device 1 = (7I + 3E + 12C + 6H + 18F + 17M)/60
Hours on test device 2 = (2I + 5E + 3C + 2H + 15F + 17M)/60
Hours on test device 3 = (5I + 1E + 3C + 2H + 9F + 2M)/60
Thus, the objective function is: Maximize profit = revenue  material cost  test cost
=
200I + 120E + 180C + 130F + 430H + 260M  35I  25E  40C  45F  170H  60M – 15(7I +
3E + 12C + 6H + 18F + 17M)/60 – 12(2I + 5E + 3C + 2H + 15F + 17M)/60 – 18(5I + 1E +
3C + 2H + 9F + 2M)/60
=
$161.35I + $92.95E + $135.50C + $82.50F + $249.80H + $191.75M
Subject to
(7I + 3E + 12C + 6H + 18F + 17M)/60
120 hours
(2I + 5E + 3C + 2H + 15F + 17M)/60
120 hours
(5I + 1E + 3C + 2H + 9F + 2M)/60
100 hours
All variables
0
Solution: See file P33.XLS.
Produce 496.55 internal modems and 1,241.38 external modems only. Profit = $195,504.83.
34.
Let J = number of Junior travel pillows to produce.
T and D defined similarly.
Objective: Maximize profit. Calculate (Revenue – Cost) for each model, and add them to obtain the total
profit. This reduces to: Profit = $1.62J + $1.33T + $1.33D
Subject to:
0.10 J
+ 0.15 T
+ 0.20 D
450
Cutting hours available
0.05 J
+ 0.12 T
+ 0.18 D
550
Sewing hours available
0.18 J
+ 0.24 T
+ 0.20 D
600
Finishing hours available
0.20 J
+ 0.20 T
+ 0.20 D
450
Packing hours available
J,
T,
D
1200
Maximum production
J,
T,
D
300
Minimum production
Solution: See file P34.XLS.
Produce 1,200 Junior, 750 Travel, and 300 Deluxe pillows. Profit = $3,340.50.
35.
Let C = number of cheese pizzas to order. P and V defined similarly.
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 Spring '10
 Bryan

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