The following diagram shows the flow process. Raw material cost, and machine processing time for three products: A, B, and C. There are three machines (W, X and Y) used in the production of these products; the times shown are in required minutes of production per unit. Raw material costs are shown in cost per unit of product. The market will take all that can be produced.   Selling price              A                       B                             C                                  $ 55                  $60                         $ 75                    $ 10----Y (2 min)  $10---Y (5 min)   $10---X (4 min)                    $ 15---W (3 min)  $20---X (5 min)   $15---Y (4 min)                    $ 15---X (2 min)    $15—W (6 min) $ 30—W (6 min)   Assuming that sales personnel are paid on a commission basis, which product should sell? A, B or C? On the basis of maximizing gross profits per unit, which product should be sold? A, B, or C 3.To maximize total profit for the firm, which product should be sold? A, B, or C?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 111P
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The following diagram shows the flow process. Raw material cost, and machine processing time for three products: A, B, and C. There are three machines (W, X and Y) used in the production of these products; the times shown are in required minutes of production per unit. Raw material costs are shown in cost per unit of product. The market will take all that can be produced.  

Selling price              A                       B                             C 

                                $ 55                  $60                         $ 75 

                  $ 10----Y (2 min)  $10---Y (5 min)   $10---X (4 min) 

                  $ 15---W (3 min)  $20---X (5 min)   $15---Y (4 min) 

                  $ 15---X (2 min)    $15—W (6 min) $ 30—W (6 min)  

  1. Assuming that sales personnel are paid on a commission basis, which product should sell? A, B or C?
  2. On the basis of maximizing gross profits per unit, which product should be sold? A, B, or C
  3. 3.To maximize total profit for the firm, which product should be sold? A, B, or C? 
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ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,