Additional Assignment #2 Problems
4.5
a)
The activities are the production rates of products 1, 2, and 3.
The limited resources
are hours available per week on the milling machine, lathe, and grinder.
b)
The decisions to be made are how many of each product should be produced per week.
The constraints on these decisions are the number of hours available per week on the
milling machine, lathe, and grinder as well as the sales potential of product 3.
The
overall measure of performance is total profit, which is to be maximized.
c)
milling machine:
9(# units of 1)
+ 3(# units of 2) + 5(# units of 3) ≤ 500
lathe:
5(# units of 1)
+ 4(# units of 2) ≤ 350
grinder:
3(# units of 1) + 2(# units of 3) ≤ 150
sales:
(# units of 3) ≤ 20
Nonnegativity:
(# units of 1) ≥ 0, (# units of 2) ≥ 0, (# units of 3) ≥ 0
Profit = $50(# units of 1) + $20(# units of 2) + $25(# units of 3)
d)
1
2
3
4
5
6
7
8
9
10
11
12
A
B
C
D
E
F
G
Product 1
Product 2
Product 3
Unit Profit
$50
$20
$25
Hours
Hours
Machine Hours Used per Unit of Product
Used
Available
Milling machine
9
3
5
500
Š
500
Lathe
5
4
0
350
Š
350
Grinder
3
0
2
118.571
Š
150
Product 1
Product 2
Product 3
Total Profit
Production Rate
26.190
54.762
20
$2,904.76
(per week)
Š
Sales Potential
20
Data cells:
B2:D2, B5:D7, G5:G7, and D12
Changing cells:
B10:D10
Target cell:
G10
Output cells:
E5:E7
3
4
5
6
7
E
Hours
Used
=SUMPRODUCT(B5:D5,$B$10:$D$10)
=SUMPRODUCT(B6:D6,$B$10:$D$10)
=SUMPRODUCT(B7:D7,$B$10:$D$10)
9
10
G
Total Profit
=SUMPRODUCT(B2:D2,B10:D10)
41
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View Full Documente)
Let
x
1
= units of product 1 produced per week
x
2
= units of product 2 produced per week
x
3
= units of product 3 produced per week
Maximize Profit = $50
x
1
+ $20
x
2
+ $25
x
3
subject to
9
x
1
3
x
2
+ 5
x
3
≤ 500 hours
5
x
1
+ 4
x
2
≤ 350 hours
3
x
1
+ 2
x
3
≤ 150 hours
x
3
≤ 20
and
x
1
≥ 0,
x
2
≥ 0,
x
3
≥ 0.
4.6
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 Winter '08
 Camateros
 Harshad number, Milling machine, $13,330, K.C. D.H. H.B. S.C. K.S. N.K, K.C. D.H. H.B. S.C. K.S. N.K.

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