Product mix problem |
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| Your company manufactures TVs, stereos and speakers, using
a common parts inventory |
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| of power supplies, speaker cones, etc. Parts are in limited supply and you must
determine |
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| the most profitable
mix of products to build. |
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TV set |
Stereo |
Speaker |
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Number to Build-> |
0 |
0 |
0 |
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| Part Name |
Inventory |
No. Used |
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| Chassis |
450 |
0 |
1 |
1 |
0 |
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| Picture Tube |
250 |
0 |
1 |
0 |
0 |
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| Speaker Cone |
800 |
0 |
2 |
2 |
1 |
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| Power Supply |
450 |
0 |
1 |
1 |
0 |
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| Electronics |
600 |
0 |
2 |
1 |
1 |
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Profits: |
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By Product |
$0 |
$0 |
$0 |
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Total |
$0 |
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| Problem |
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| Your
company builds TVs, stereos and speakers, using a common parts inventory of
power supplies, |
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| speaker
cones, etc. Parts are in limited supply. What is the best combination of
products to build |
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| that maximizes
profit? |
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| Solution |
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| 1)
The variables are clearly the number of TVs, stereos and speakers to build.
In this worksheet, they |
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| are given the
name Number_to_build. |
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| 2) The constraints specify that the number of parts used
cannot exceed the supply. This leads to |
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Number_used
<= Number_available |
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| There is also
the logical constraint |
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Number_to_build >= 0 via the Assume Non-Negative option |
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| 3) The objective is to maximize profit. In the ProductMix
worksheet this is defined as Total_profit. |
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| Remarks |
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| Although
this is a good example of a product mix problem, bear in mind the limitations
of the |
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| model.
For example, market demand and price elasticity is not included in the model
-- we assume |
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it doesn't matter how many TVs we build, we will always be able to sell them.
Nor are there any |
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| pre-specified
minimum or maximum of products that need to be made. The effect of
introducing |
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| these
restrictions can be studied by examining a Sensitivity Report, which you can
select from the |
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| dialog appears
with the message 'Solver found a solution.' |
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