b) If the profit per unit of product 2 increased by GHC 2 to GHC 22, would the optimal production quantities of products 2 and 3 change? Would the optimal value of the objective function change? c) If the available amount of material increased by 10 pounds to 210 pounds, how would that affect the optimal value of the objective function d) Which resource(s) is/are efficiently used at the optimal? Justify
b) If the profit per unit of product 2 increased by GHC 2 to GHC 22, would the optimal production quantities of products 2 and 3 change? Would the optimal value of the objective function change? c) If the available amount of material increased by 10 pounds to 210 pounds, how would that affect the optimal value of the objective function d) Which resource(s) is/are efficiently used at the optimal? Justify
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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Transcribed Image Text:b) If the profit per unit of product 2 increased by GHC 2 to GHC 22, would the
optimal production
quantities of products 2 and 3 change? Would the optimal value of the
objective function change?
c) If the available amount of material increased by 10 pounds to 210 pounds, how
would that affect the optimal value of the objective function
d) Which resource(s) is/are efficiently used at the optimal? Justify
Transcribed Image Text:Question 1
The linear programming model below was solved by computer
Маximize Z 3D 5х, + 20х2 + 14xз
Subject to:
Labour 5x1 + 6x2+ 4x3 < 210 hours
Machine 4x1 + 2x2 + 5x3< 170 minutes
Material 10x,+8x2+ 5x3< 200 pounds
X1,X2,X3 2 0
where x1 = quantity of product 1
X2 = quantity of product 2
X3 = quantity of product 3
The following information was obtained from the output.
Total profit = 548.00
Variable
value Reduced cost
Range of Optimality
Product 1
10.6
unlimited to 25.60
Product 2 5
9.40 to
22.40
Product 3
32
12.50 to
50.00
Constraint Slack Shadow price
Range of Feasibility
Labour
52
0.0
158.00 to unlimited
Material
2.4
170.00 to 270.91
Machine
0.4
50.00 to 200.0
a) By how much would the profit per unit of product 1 have to increase in order
for it to have a none-zero value?
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