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Saint COm315 problems

Chapter 5. Transportation, Assignment; and Network Models

The Southern Rail Company ships coal by rail from three coal mines to meet the demand requirementsof four coal depots. The following table shows the distances from the mines to the various depots and the availabilities and requirements for coal. Determine the best shipment of coal cars to minimize the total miles traveled by the cars. = 3100 miles

To

From

Columbia

Albany

Springfield

Pleasantburg

Supply of cars

Paris

50

30

60

70

35

Butler

20

80

10

90

60

Century

100

40

80

30

25

Demand for cars

30

45

25

20

Chapter 6. Integer Programming

A hospital is planning an $8 million addition to its existing facility. The architect has been asked toconsider 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 room of each type should the architect include in the new hospital design?

Chapter 7. Project Management

A plant engineering group needs to set up an assembly line to produce a new product. The table included 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 completiontime 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.

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