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 $41, $39, $42, $38, and $39 in Plants 1, 2, 3, 4, and 5, respectively. The unit manufacturing cost of the second product would be $55, $51, $56, $52, and $53 in Plants 1, 2, 3, 4, and 5, respectively. The unit manufacturing cost of the third product would be $48, $45, and $50 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 700, 1,000, and 900 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. (b) Use Excel Solver to obtain an optimal solution.
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 $41, $39, $42, $38, and $39 in Plants 1, 2, 3, 4, and 5, respectively. The unit manufacturing cost of the second product would be $55, $51, $56, $52, and $53 in Plants 1, 2, 3, 4, and 5, respectively. The unit manufacturing cost of the third product would be $48, $45, and $50 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 700, 1,000, and 900 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. (b) Use Excel Solver to obtain an optimal solution.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
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Transcribed Image Text: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 $41, $39, $42, $38, and $39 in
Plants 1, 2, 3, 4, and 5, respectively. The unit manufacturing cost of the second product would be $55, $51,
$56, $52, and $53 in Plants 1, 2, 3, 4, and 5, respectively. The unit manufacturing cost of the third product
would be $48, $45, and $50 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 700, 1,000, and 900 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.
(b) Use Excel Solver to obtain an optimal solution.
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