Industrial Designs has been awarded a contract to design a label for a new wine
ID: 449271 • Letter: I
Question
Industrial Designs has been awarded a contract to design a label for a new wine produced by Princess M Wineries. The company estimates that 150 hours will be required to complete the project. The firm will use three designers on the project: Lisa is a senior designer and team leader, David a senior designer, and Sarah, a junior designer. Lisa is the most experienced designer and she must be assigned at least 40% of the hours assigned to the two senior designers. Sarah needs experience and she must be assigned at least 15% of the project's hours. But, Sarah must be assigned less than 25% of the total hours assigned to the two senior designers. Due to other project committments, Lisa has a maximum of 50 hours available to work on this project. Hourly rates are $30 for Lisa, $25 for David, $18 for Sarah.
a. Write a linear program model that can be used to determine the number of hours each designer should be assigned to the project to minimize costs.
b. How many hours should each designer be assigned? What is the total cost?
Explanation / Answer
Let x1, x2 and x3 stands for Lisa david and sarah
The objective of the firm is to minimise total cost . So the objective funtions
Min Z = 30X1+25X2+18X3
Subject to
x1>= 0.4*(x2+x3)
I.e x1-0.4x2-0.4x3>=0
Lisa must be available for 40% of the time of the two desingers
x3>=0.15*150
I.e x3>=22.5
( Sarah need atleast 15% of the total time)
x3<=0.25*(x1+x2)
I.e x3-0.25x1-0.25x2<=0
I.e 0.25x1+0.25x2-x3>=0
Sarah must be assigned less than 25 % of two senior designer time)
x1+x2+x3<=150
Total time for all th three is 150 hours
The solver solution for the above problem is given given below.
Min Z 2815.714 X1 32.14286 X2 57.85714 X3 22.5 Constraints 0 0 >= 22.5 22.5 >= 0 0 >= 112.5 150 <=