A clothing company manufactures coats, pants, gloves, and hats for the winter season. All products are manufactured in four different departments: cutting, insulating, sewing, and packaging. According to firm orders, the contract stipulates a penalty for undelivered items. Considering the data in the table, formulate the problem to obtain an optimal production plan. Food Cutting Insulating Sewing Packaging Demand (units) Unit profit ($) Unit penalty ($) Coats (hr/unit) 0,30 0,25 0,45 0,15 800 30 15 Pants (hr/unit) 0,30 0,35 0,50 0,15 750 40 20 Gloves (hr/unit) 0,25 0,30 0,40 0,10 600 20 10 Hats (hr/unit) 0,15 0,10 0,22 0,05 500 10 8 Capacity (hr) 1000 800 1200 1080

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A clothing company manufactures coats, pants, gloves, and hats for the winter season. All
products are manufactured in four different departments: cutting, insulating, sewing, and
packaging. According to firm orders, the contract stipulates a penalty for undelivered items.
Considering the data in the table, formulate the problem to obtain an optimal production plan.
Food
Cutting
Insulating
Sewing
Packaging
Demand (units)
Unit profit ($)
Unit penalty ($)
Coats
(hr/unit)
0,30
0,25
0,45
0,15
800
30
15
Pants
(hr/unit)
0,30
0,35
0,50
0,15
750
40
20
Gloves
(hr/unit)
0,25
0,30
0,40
0,10
600
20
10
Hats
(hr/unit)
0,15
0,10
0,22
0,05
500
10
Mathematical model:
Indexes
i = 1, 2, 3, 4 (products, respectively)
Decision variables
x: The number of ith product to be produced
st: The demand for ith product which is not met
Model
Max z = 30x₁ + 40x2 + 20x3 + 10x4 (15s₁ +20s2 + 1053 +854)
St, 0,30x, +0,30x2 +0,25x3 + 0,15x4≤ 1000
0,25x₁ +0,35x2 + 0,30x3 + 0,10x4 ≤ 800
0,45x₁ + 0,50x2 +0,40x3 + 0,22x4≤ 1200
0,15x₁ +0,15x₂ + 0,10x3 + 0,05x4 S 1080
X₂ + $₂ = 750
X₁ + S₁ = 800
X3 + S3 = 600
X4+S4= 500
X, 20
Capacity (hr)
1000
800
1200
1080
Transcribed Image Text:A clothing company manufactures coats, pants, gloves, and hats for the winter season. All products are manufactured in four different departments: cutting, insulating, sewing, and packaging. According to firm orders, the contract stipulates a penalty for undelivered items. Considering the data in the table, formulate the problem to obtain an optimal production plan. Food Cutting Insulating Sewing Packaging Demand (units) Unit profit ($) Unit penalty ($) Coats (hr/unit) 0,30 0,25 0,45 0,15 800 30 15 Pants (hr/unit) 0,30 0,35 0,50 0,15 750 40 20 Gloves (hr/unit) 0,25 0,30 0,40 0,10 600 20 10 Hats (hr/unit) 0,15 0,10 0,22 0,05 500 10 Mathematical model: Indexes i = 1, 2, 3, 4 (products, respectively) Decision variables x: The number of ith product to be produced st: The demand for ith product which is not met Model Max z = 30x₁ + 40x2 + 20x3 + 10x4 (15s₁ +20s2 + 1053 +854) St, 0,30x, +0,30x2 +0,25x3 + 0,15x4≤ 1000 0,25x₁ +0,35x2 + 0,30x3 + 0,10x4 ≤ 800 0,45x₁ + 0,50x2 +0,40x3 + 0,22x4≤ 1200 0,15x₁ +0,15x₂ + 0,10x3 + 0,05x4 S 1080 X₂ + $₂ = 750 X₁ + S₁ = 800 X3 + S3 = 600 X4+S4= 500 X, 20 Capacity (hr) 1000 800 1200 1080
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