9.1-3. The Versatech Corporation has decided to produce three new products. Five branch plants now have excess product capacity. The unit manufacturing cost of the first product would be $31, $29, $32, $28, and $29 in Plants 1, 2, 3, 4, and 5, respectively. The unit manufacturing cost of the second product would be $45, $41, $46, $42, and $43 in Plants 1, 2, 3, 4, and 5, respectively. The unit manufacturing cost of the third product would be $38, $35, and $40 in Plants 1, 2, and 3, respectively, whereas Plants 4 and 5 do not have the capability for producing this product. Sales forecasts indicate that 600, 1,000, and 800 units of products 1, 2, and 3, respectively, should be produced per day. Plants 1, 2, 3, 4, and 5 have the capacity to produce 400, 600, 400, 600, and 1,000 units daily, respectively, regardless of the product or combination of products involved. Assume that any plant having the capability and capacity to produce them can produce any combination of the products in any quantity. Management wishes to know how to allocate the new products to the plants to minimize total manufacturing cost. (a) Formulate this problem as a transportation problem by constructing the appropriate parameter table. c (b)Obtain an optimal solution.
9.1-3. The Versatech Corporation has decided to produce three new products. Five branch plants now have excess product capacity. The unit manufacturing cost of the first product would be $31, $29, $32, $28, and $29 in Plants 1, 2, 3, 4, and 5, respectively. The unit manufacturing cost of the second product would be $45, $41, $46, $42, and $43 in Plants 1, 2, 3, 4, and 5, respectively. The unit manufacturing cost of the third product would be $38, $35, and $40 in Plants 1, 2, and 3, respectively, whereas Plants 4 and 5 do not have the capability for producing this product. Sales forecasts indicate that 600, 1,000, and 800 units of products 1, 2, and 3, respectively, should be produced per day. Plants 1, 2, 3, 4, and 5 have the capacity to produce 400, 600, 400, 600, and 1,000 units daily, respectively, regardless of the product or combination of products involved. Assume that any plant having the capability and capacity to produce them can produce any combination of the products in any quantity. Management wishes to know how to allocate the new products to the plants to minimize total manufacturing cost. (a) Formulate this problem as a transportation problem by constructing the appropriate parameter table. c (b)Obtain an optimal solution.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:9.1-3. The Versatech Corporation has decided to produce three new products. Five branch
plants now have excess product capacity. The unit manufacturing cost of the first product
would be $31, $29, $32, $28, and $29 in Plants 1, 2, 3, 4, and 5, respectively. The unit
manufacturing cost of the second product would be $45, $41, $46, $42, and $43 in Plants
1, 2, 3, 4, and 5, respectively. The unit manufacturing cost of the third product would be
$38, $35, and $40 in Plants 1, 2, and 3, respectively, whereas Plants 4 and 5 do not have
the capability for producing this product. Sales forecasts indicate that 600, 1,000, and 800
units of products 1, 2, and 3, respectively, should be produced per day. Plants 1, 2, 3, 4,
and 5 have the capacity to produce 400, 600, 400, 600, and 1,000 units daily, respectively,
regardless of the product or combination of products involved. Assume that any plant
having the capability and capacity to produce them can produce any combination of the
products in any quantity.
Management wishes to know how to allocate the new products to the plants to
minimize total manufacturing cost.
(a) Formulate this problem as a transportation problem by constructing the appropriate
parameter table.
c (b)Obtain an optimal solution.
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