Minimum Number of Consultants Required to Be on Duty Time of Day 8 AM-noon Noon-4 PM 4 PM-8 PM 8 12 8 PM-midnight Two types of computer consultants can be hired: full-time and part-time. The full-time consultants work for eight consecu- tive hours in any of the following shifts: morning (8 AM-4 PM), afternoon (noon-8 PM), and evening (4 PM-midnight). Full-time consultants are paid $14 per hour. Part-time consultants can be hired to work any of the four shifts listed in the table. Part-time consultants are paid $12 per hour. An additional requirement is that during every time period, there must be at least two full-time consultants on duty for every part-time consultant on duty. Larry would like to determine how many full-time and part- time consultants should work each shift to meet the above requirements at the minimum possible cost. a. Which category of linear programming problem does this problem fit? Why? E* b. Formulate and solve a linear programming model for this problem on a spreadsheet. c. Summarize the model in algebraic form.
Minimum Number of Consultants Required to Be on Duty Time of Day 8 AM-noon Noon-4 PM 4 PM-8 PM 8 12 8 PM-midnight Two types of computer consultants can be hired: full-time and part-time. The full-time consultants work for eight consecu- tive hours in any of the following shifts: morning (8 AM-4 PM), afternoon (noon-8 PM), and evening (4 PM-midnight). Full-time consultants are paid $14 per hour. Part-time consultants can be hired to work any of the four shifts listed in the table. Part-time consultants are paid $12 per hour. An additional requirement is that during every time period, there must be at least two full-time consultants on duty for every part-time consultant on duty. Larry would like to determine how many full-time and part- time consultants should work each shift to meet the above requirements at the minimum possible cost. a. Which category of linear programming problem does this problem fit? Why? E* b. Formulate and solve a linear programming model for this problem on a spreadsheet. c. Summarize the model in algebraic form.
Chapter19: Pricing Concepts
Section: Chapter Questions
Problem 6DRQ
Related questions
Question
need the answers for 3.15 and 3.16
Transcribed Image Text:of
Chapter 3 Problems
103
ld
The objective is to minimize the total leasing cost for meet-
ing the space requirements.
Minimum Number of
a. Indicate why this is a cost-benefit-trade-off prob-
lem by identifying both the activities and the bene-
fits being sought from these activities.
Consultants Required
to Be on Duty
Time of Day
8 AM-noon
b. Identify verbally the decisions to be made, the con-
straints on these decisions, and the overall measure
of performance for the decisions.
c. Convert these verbal descriptions of the constraints
and the measure of performance into quantitative
expressions in terms of the data and decisions.
d. Formulate a spreadsheet model for this problem.
Identify the data cells, the changing cells, the target
cell, and the other output cells. Also show the Excel
equation for each output cell expressed as a
SUMPRODUCT function. Then use the Excel
Solver to solve the model.
Noon-4 PM
8.
4 PM-8 PM
12
8 PM-midnight
6
Two types of computer consultants can be hired: full-time
and part-time. The full-time consultants work for eight consecu-
tive hours in any of the following shifts: morning (8 AM-4 PM),
afternoon (noon-8 PM), and evening (4 PM-midnight). Full-time
consultants are paid $14 per hour.
Part-time consultants can be hired to work any of the four shifts
listed in the table. Part-time consultants are paid $12 per hour.
An additional requirement is that during every time period,
there must be at least two full-time consultants on duty for every
part-time consultant on duty.
Larry would like to determine how many full-time and part-
E*
e.
Summarize the model in algebraic form.
E*3.14. Consider the following algebraic formulation of a
cost-benefit-trade-off problem involving three benefits, where
the decisions to be made are the levels of four activities (A1, A2,
A3, and A4):
time consultants should work each shift to meet the above
requirements at the minimum possible cost.
Minimize Cost 2 A, + A2 - A3 + 3 A4
a. Which category of linear programming problem
does this problem fit? Why?
b. Formulate and solve a linear programming model
for this problem on a spreadsheet.
c. Summarize the model in algebraic form.
3.16.* The Medequip Company produces precision med-
ieal diagnostic equipment at two factories. Three medical
centers have placed orders for this month's production out-
put. The following table shows what the cost would be for
shipping each unit from each factory to each of these cus-
tomers. Also shown are the number of units that will be pro-
duced at each factory and the number of units ordered by
subject to
E*
Benefit 1: 3 A,+2 A2-2 A3+5 A4 > 80 (minimum
acсeptable
level)
+ A4> 10 (minimum
Benefit 2:
A1- A2
acсеptable
level)
A1 + A2- A, + 2A42 30 (minimum
acceptable
level)
Benefit 3:
each customer.
and
A decision now needs to be made about the shipping
A, 20 A, 2 0 A4 2 0
plan for how many units to ship from each factory to each
customer.
Formulate and solve the spreadsheet model for this problem.
Unit Shipping Cost
To
From
Customer 1
Customer 2
Customer 3
Output
$700
400 units
Factory 1
Factory 2
$600
$800
400
900
600
500 units
Order size
300 units
200 units
400 units
a. Which category of linear programming problem
does this problem fit? Why?
b. Formulate and solve a linear programming model
for this problem on a spreadsheet.
c. Summarize this formulation in algebraic form.
E*
Larry Edison is the Director of the Computer Center for
3.15
Buckly College. He now needs to schedule the staffing of the
center. It is open from 8 AM until midnight. Larry has monitored
the usage of the center at various times of the day and deter-
mined that the following number of computer consultants are
required:
The Fagersta Steelworks currently is working two
mines to obtain its iron ore. This iron ore is shipped to either of
two storage facilities. When needed, it then is shipped on to the
3.17.
s from
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 3 images
