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Formulate a linear programming problem that can be used to solve the following question. A company has three plants that produce three different sizes of their product. The North plant can produce 2000 items in the small size, 2000 in the medium size, and 1000 in the large size. The Center plant can produce 1000 items in the small size, 2000 in the medium size, and 2000 in the large size. The South plant can produce 1000 items in the small size, 1000 in the medium size, and 1000 in the large size. The company needs to produce at least 8000 of the small items, 9000 of the medium items, and 7000 of the large items on a given day. The cost of producing the small item is $3, the medium item $5, and the large item $4. Find the number of items each plant should produce in order to minimize the cost. Let X₁, X2, and x3 be the number of small, medium, and large items produced by the North Plant, respectively. Let Y₁, V2, and y3 be the number of small, medium, and large items produced by the Center Plant, respectively. Let Z₁, Z2, and 23 be the number of small, medium, and large items produced by the South Plant. ---Select---|F= Subject to (objective function) (small items) (medium items) (large items) (North Plant small items) (North Plant medium items) (North Plant large items) (Center Plant small items) (Center Plant medium items) (Center Plant large items) (South Plant small items) (South Plant medium items) (South Plant large items)

Formulate a linear programming problem that can be used to solve the following question. A company has three plants that produce three different sizes of their product. The North plant can produce 2000 items in the small size, 2000 in the medium size, and 1000 in the large size. The Center plant can produce 1000 items in the small size, 2000 in the medium size, and 2000 in the large size. The South plant can produce 1000 items in the small size, 1000 in the medium size, and 1000 in the large size. The company needs to produce at least 8000 of the small items, 9000 of the medium items, and 7000 of the large items on a given day. The cost of producing the small item is $3, the medium item $5, and the large item $4. Find the number of items each plant should produce in order to minimize the cost. Let X₁, X2, and x3 be the number of small, medium, and large items produced by the North Plant, respectively. Let Y₁, V2, and y3 be the number of small, medium, and large items produced by the Center Plant, respectively. Let Z₁, Z2, and 23 be the number of small, medium, and large items produced by the South Plant. ---Select---|F= Subject to (objective function) (small items) (medium items) (large items) (North Plant small items) (North Plant medium items) (North Plant large items) (Center Plant small items) (Center Plant medium items) (Center Plant large items) (South Plant small items) (South Plant medium items) (South Plant large items)

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 32E
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Formulate a linear programming problem that can be used to solve the following question. A company has three plants that produce three different sizes of their product. The North plant can produce 2000 items in the small size, 2000 in the medium size, and 1000 in the large size. The Center plant can produce 1000 items in the small size, 2000 in the medium size, and 2000 in the large size. The South plant can produce 1000 items in the small size, 1000 in the medium size, and 1000 in the large size. The company needs to produce at least 8000 of the small items, 9000 of the medium items, and 7000 of the large items on a given day. The cost of producing the small item is $3, the medium item $5, and the large item $4. Find the number of items each plant should produce in order to minimize the cost. Let X₁, X₂, and x3 be the number of small, medium, and large items produced by the North Plant, respectively. Let Y₁, 2, and y3 be the number of small, medium, and large items produced by the Center Plant, respectively. Let Z₁, Z2, and z3 be the number of small, medium, and large items produced by the South Plant. ---Select--- ✓ F = Subject to (objective function) (small items) (medium items) (large items) (North Plant small items) (North Plant medium items) (North Plant large items) (Center Plant small items) (Center Plant medium items) (Center Plant large items) (South Plant small items) (South Plant medium items) (South Plant large items)
Transcribed Image Text:Formulate a linear programming problem that can be used to solve the following question. A company has three plants that produce three different sizes of their product. The North plant can produce 2000 items in the small size, 2000 in the medium size, and 1000 in the large size. The Center plant can produce 1000 items in the small size, 2000 in the medium size, and 2000 in the large size. The South plant can produce 1000 items in the small size, 1000 in the medium size, and 1000 in the large size. The company needs to produce at least 8000 of the small items, 9000 of the medium items, and 7000 of the large items on a given day. The cost of producing the small item is $3, the medium item $5, and the large item $4. Find the number of items each plant should produce in order to minimize the cost. Let X₁, X₂, and x3 be the number of small, medium, and large items produced by the North Plant, respectively. Let Y₁, 2, and y3 be the number of small, medium, and large items produced by the Center Plant, respectively. Let Z₁, Z2, and z3 be the number of small, medium, and large items produced by the South Plant. ---Select--- ✓ F = Subject to (objective function) (small items) (medium items) (large items) (North Plant small items) (North Plant medium items) (North Plant large items) (Center Plant small items) (Center Plant medium items) (Center Plant large items) (South Plant small items) (South Plant medium items) (South Plant large items)
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