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 firm’s 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, $16 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. For negative numbers use a minus sign (Example: enter -100). Let L = number of hours assigned to Lisa D = number of hours assigned to David S = number of hours assigned 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. There lower limit on the right-hand-side range, so the optimal solution change.

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 firm’s 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, $16 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. For negative numbers use a minus sign (Example: enter -100). Let L = number of hours assigned to Lisa D = number of hours assigned to David S = number of hours assigned 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. There lower limit on the right-hand-side range, so the optimal solution change.

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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(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. For negative numbers use a minus sign (Example: enter -100).

Let L	= number of hours assigned to Lisa
D	= number of hours assigned to David
S	= number of hours assigned 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.

There lower limit on the right-hand-side range, so the optimal solution change.

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