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You are given a linear programming problem. Maximize      P = 6x + 4y subject to   2x  +  3y  ≤ 12      Resource 1   2x  +  y  ≤ 8   Resource 2       y  ≥ 0         x  ≥ 0   (a) Use the method of corners to solve the problem. The maximum is P =  at  (x, y) =              . (b) Suppose P = cx + 4y. Find the range of values that the coefficient c of x can assume without changing the optimal solution.  ≤ c ≤  (c) Find the range of values that Resource 1 can assume.  ≤ (Resource 1) ≤  (d) Find the shadow price for Resource 1. (e) Identify the binding and nonbinding constraints. constraint 1          constraint 2

You are given a linear programming problem. Maximize      P = 6x + 4y subject to   2x  +  3y  ≤ 12      Resource 1   2x  +  y  ≤ 8   Resource 2       y  ≥ 0         x  ≥ 0   (a) Use the method of corners to solve the problem. The maximum is P =  at  (x, y) =              . (b) Suppose P = cx + 4y. Find the range of values that the coefficient c of x can assume without changing the optimal solution.  ≤ c ≤  (c) Find the range of values that Resource 1 can assume.  ≤ (Resource 1) ≤  (d) Find the shadow price for Resource 1. (e) Identify the binding and nonbinding constraints. constraint 1          constraint 2

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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You are given a linear programming problem.

Maximize      P = 6x + 4y

subject to   2x  +  3y  ≤ 12      Resource 1
  2x  +  y  ≤ 8   Resource 2
      y  ≥ 0  
      x  ≥ 0  
(a) Use the method of corners to solve the problem.
The maximum is P =  at 
(x, y) = 
 
 
 
 
 
 
 
.
(b) Suppose P = cx + 4y. Find the range of values that the coefficient c of x can assume without changing the optimal solution.
 ≤ c ≤ 


(c) Find the range of values that Resource 1 can assume.
 ≤ (Resource 1) ≤ 


(d) Find the shadow price for Resource 1.


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