Linear Programming Model

Problem P 6-16

A hospital is planning an $8 million addition to its
existing facility. The architect has been asked to con-
sider the following design parameters: (1) There should
be at least 10 and no more than 20 intensive care unit
(ICU) rooms; (2) there should be at least 10 and no

more than 20 cardiac care unit (CCU) rooms; (3) there
should be no more than 50 double rooms; (4) there
should be at least 35 single rooms; and (5) all patient
rooms should fit inside the allotted 40,000-square-foot
space (not including hallways). The following table
summarizes the relevant room data:
SINGLE DOUBLE ICU CCU
Cost per room to build and furnish ($thousands) $45 $54 $110 $104
Minimum square feet required 300 360 320 340
Profit per room per month ($thousands) $21 $28 $ 48 $ 41

How many rooms of each type should the architect
include in the new hospital design?

Problem P 6-30

6-30 Sandy Edge is president of Edge File Works, a
firm that manufactures two types of metal file
cabinets. The demand for the two-drawer model
is 650 cabinets per week; demand for the three-
drawer cabinet is 400 per week. Edge has a weekly
operating capacity of 1,600 hours, with the two-
drawer cabinet taking 1.5 hours to produce and
the three-drawer cabinet requiring 2 hours. Each
two-drawer model sold yields a $12 profit, and
the profit for the three-drawer model is $14. Edge
has listed the following goals, in rank order:
Rank 1: Attain a profit as close to $12,000 as pos-
sible each week.
Rank 2: Avoid underutilization of the firm’s pro-
duction capacity.
Rank 3: Sell as many two- and three-drawer cabi-
nets as the demand indicates.
Set up and solve this problem as a goal program-
ming model.

Problem 7-18

7-18 A plant engineering group needs to set up an assem-
bly line to produce a new product. The table in the
next column describes the relationships between the
activities that need to be completed for this product
to be manufactured.
(a) Develop a project network for this problem.
(b) Determine the expected duration and variance
for each activity.

(c) Determine the EST, EFT, LST, LFT, and slack
for each activity. Also determine the total project
completion time and the critical path(s).
(d) Determine the probability that the project will be
completed in less than 34 days.
(e) Determine the probability that the project will
take more than 29 days.

ACTIVITY DAYS IMMEDIATE
PREDECESSORSa m b

Problem 7-18
Activity Pred Optim time (a) Most likely time (m) Pessim time (b) Expected time Variance Standard deviation EST EFT LST LFT Slack Critical?
0.00 0.00 0.00 0.00 0.00 Y
0.00 0.00 0.00 0.00 0.00 Y
Y
Y
Y
Y
Y