Industrial Designs has been awarded a contract to design a label for a new wine produced…

Industrial Designs has been awarded a contract to design a label
for a new wine produced by Lake View Winery. The company estimates
that 150 hours will be required to complete the project. The firms
three graphic designers available for assignment to this project
are 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 label designing
experience for Sarah, the junior designer 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 maximum of 50 hours available to work on
this project. Hourly wage rates are $30 for Lisa, $15 for David,
and $18 for Sarah.

(a)
Formulate a linear program that can be used to determine the
number of hours each graphic designer should be assigned to the
project to minimize total cost. If an amount is zero, enter 0. If
the constant is “1” it must be entered in the box.

Let L
= number of hours assigned to Lisa

D
= number of hours assigned to David

S
= amount allocated to Sarah

Min
L
+
D
+
S

s.t.

L
+
D
+
S
_

Minimum Lisa

L
+
D
+
S
_

Minimum Sarah

L
+
D
+
S
_

Maximum Lisa

L
+
D
+
S
_

Maximum Sarah

L
+
D
+
S
=

Total Time

L, D, S
_
0

(b)
How many hours should be assigned to each graphic
designer?

Hours Assigned

Lisa

David

Sarah

What is the total cost? If required, round your answer to a
whole dollar amount.

$

(c)
Suppose Lisa could be assigned more than 50 hours. What effect
would this have on the optimal solution? Explain. If an amount is
zero, enter 0.

We know that the shadow price for this constraint is , since
the constraint is

. Therefore, additional hours for Lisa will

the solution.

(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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