model B. To produce each model A grate requires 3 pounds of cast iron and 6 minutes of labor. To produce each model B grate requires 4 pounds of cast iron and 3 minutes of labor. The profit for each model A grate is $1.75, and the profit for each model B grate is $1.25. Available for grate production each day are 1000 pounds of cast iron and 20 labor-hours. Because of an excess inventory of model A grates, management has decided to limit the production of model A grates to no more than 180 grates per day. Maximize      P = 1.75x + 1.25y subject to   3x  +  4y  ≤ 1000      Resource 1   6x  +  3y  ≤ 1200   Resource 2       x  ≤ 180   Resource 3       y  ≥ 0         x  ≥ 0   (a) Find the shadow price for Resource 2. (Round your answer to the nearest cent.) $  (b) Identify the binding and nonbinding constraints. constraint 1          constraint 2       constraint 3

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Kane Manufacturing has a division that produces two models of grates, model A and model B. To produce each model A grate requires 3 pounds of cast iron and 6 minutes of labor. To produce each model B grate requires 4 pounds of cast iron and 3 minutes of labor. The profit for each model A grate is $1.75, and the profit for each model B grate is $1.25. Available for grate production each day are 1000 pounds of cast iron and 20 labor-hours. Because of an excess inventory of model A grates, management has decided to limit the production of model A grates to no more than 180 grates per day.

Maximize      P = 1.75x + 1.25y

subject to   3x  +  4y  ≤ 1000      Resource 1
  6x  +  3y  ≤ 1200   Resource 2
      x  ≤ 180   Resource 3
      y  ≥ 0  
      x  ≥ 0  
(a) Find the shadow price for Resource 2. (Round your answer to the nearest cent.)


(b) Identify the binding and nonbinding constraints.
constraint 1         
constraint 2      
constraint 3      
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