Quantiative Methods
posted by Sharon on .
Industrial Designs has been awarded a contract to design a label for a new wine produced by Lake View Winery. The Co estimates that 150 hours will be required to complete the project. The firm's three graphics designers available for assisgment to this project ar Lisa, a senior designer and team leader: David, a senior designer, and Sarah a junior designer. Because Lisa has worked on several projects for Lake View Winery, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers. to provide labeldesigning experience for Sarah,Sarah must be assigned at least 15% of the total project time. However, the number of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers. Due to other project commitments, Lisa has a maximim of 50 hours available to work on this project. Hourly wage rates are $ 30 for Lisa, $25 for David, and $18 for Sarah.
Now:
(a) Formulate a linear program that can be used to determine the number of hours each graphic designer should be assigned to the project in order to minimize total cost.
(b) How many hours should each graphic designer be assigned to the project? What is the total cost?
(c) Suppose Lisa could be assigned more than 50hours. What effect would this have on the optimal solution? Explain
(d) If Sarah were not required to work a minimum number of hours on this project, would the optimal solution change? Explain

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a.
Let L = # of hours assigned to Lisa
D = # of hours assigned to David
S = # of hours assigned to Sarah
Max 30L + 25D + 18S
s.t.
L + D + S = 100
0.6L  0.4D >= 0
0.15L  0.15D + 0.85S >= 0
0.25L  0.25D + S <= 0
L <= 50 
a).
Let L = # of hours assigned to Lisa
D = # of hours assigned to David
S = # of hours assigned to Sarah
Max 30L + 25D + 18S
s.t.
L + D + S = 100
0.6L  0.4D >= 0
0.15L  0.15D + 0.85S >= 0
0.25L  0.25D + S <= 0
L <= 50
L , D , S >= 0
b).
L = 48 Hours
D = 72 Hours
S = 30 Hours
Total Cost = $3780
c).
The Dual Price for Constraint 5 is 0. Therefore, additional hours for Lisa will not change the solution
d).
The dual price for constraint 3 is 0. Because there is No Lower Limit on the right and side range, the optimal solution will not change. Resolving the problem without this constraint will also show that the solution obtained in (b) does not change. Constraint 3, therefore, is really a redundant constraint. 
You are supposed to minimize this problem, not maximize it.
L= 32
D= 48
S= 20
cost= $2,520 
No Greg, the answer is 3780. You are supposed to minimize it though. That was the answer in the back of the book.