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Problem 8-1 Template
8-1 (Production problem) Winkler Furniture manufactures two different types of china cabinets: a French Provincial
model and a Danish Modern model. Each cabinet produced must go through three departments: carpentry, painting,
and finishing. The table below contains all relevant information concerning production times per cabinet produced
and production capacities for each operation per day, along with net revenue per unit produced. The firm has a
contract with an Indiana distributor to produce a minimum of 300 of each cabinet per week (or 60 cabinets per day).
Owner Bob Winkler would like to determine a product mix to maximize his daily revenue.
(a) Formulate as an LP problem.
(b) Solve using an LP software program or spreadsheet.
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10 Inputs
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Carpentry
Painting
Finishing
Cabinet Style
(hours/cabinet)
(hours/cabinet)
(hours/cabinet) Net Revenue/Cabinet ($)
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French Provincial (X1)
3.0
1.5
0.75
$28
Danish Modern (X2)
2.0
1.0
0.75
$25
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Department Capacity (hours)
360
200
125
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Place the Optimal quantities here
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# Cabinets
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French Provincial (X1)
60
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Danish Modern (X2)
90
Place the Constraint equations here
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22 Constraints
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Constraints
Requirement
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Carpentry Department
360
<=
360
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Painting Department
180
<=
200
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Finishing Department
112.5
<=
125
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Contract Requirement X1
60
>=
60
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Contract Requirement X2
90
>=
60
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31 Objective to maximize
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Revenue
$3,930
Place the computed Revenue value here
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Carpentory Hours
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3hours/french provincial . X1 french provinacials + 2
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Optimal Solution: X1 = 60 X2 = 90 Revenue = $3,930
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Problem 2.3
Solve using the Corner Point Method here.
X2
X1