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OPRE 3333 (Johnston)

Spring 2016

Homework 7

DUE: 3 April 2016

Use the EXCEL Solver to solve the following optimization problems. Be prepared

to identify the type of problem (minimization or maximization), the final value of

the Objective Function, some or all of the final values for Decision Variables,

some or all of the constraints, some or all of the Shadow Prices, and to answer

other pertinent questions related to each of the scenarios.

It is recommended that at least EXCEL 2010 (PC) or 2013 (Mac) be used for this

homework. Standard SIMPLEX Linear Programming models should be run in all

cases. Integer constraints should not be used except where BINARY variables are

indicated.

Each answer is worth 20 points.

Your answers are to be provided through the HW 7 assessment in eLearning for

this course and section.

1. A small manufacturing operation (SMO) produces six kinds of

parts (P-1, P-2, P-3, P-4, P-5, P-6), using three machines (M-1, M2, M-3). For the coming month, a certain number of each part is

needed (P-1 = 10, P-2 = 40, P-3 = 60, P-4 = 20, P-5 = 20, and P-6

= 30). Each machine can produce any part for which a cost is

listed, but has a maximum monthly output of parts (M-1 = 80, M-2

= 30, and M-3 = 160). It does not cost the same amount to make

the same part on different machines (the parts manufacturing cost

for each part on each machine is given later in this document).

How many of each part should be produced on each machine?

2. Tree Top Airways has a cargo plane with three compartments for

storage: front, center and rear. The weight and space limits for

these compartments are listed in a table later in this document. To

maintain proper operating characteristics, the loaded weights of the

compartments must each be in the same relationship as their

respective weight capacities. Four cargos, which may be mixed,

are available for shipment on the next flight. These cargos, with

their total weights, volume per ton, and profit per ton are listed in

another table later in this document. How much cargo can be

carried safely for the maximum total profit?

3. The CFO of your company has determined that the firm?s capital

investment budget will be limited to \$3,000,000 for the upcoming

year. Unfortunately, this amount is not sufficient to cover all of

the proposed projects under consideration at the firm. Each

potential project is labeled with a single letter (A-J). The

calculated values (NPV) for each project, in order are: \$72,658 ;

\$36,418 ; \$212,150 ; \$70,925 ; \$11,400 ; \$56,842 ; \$93,600 ;

\$65,350 ; \$48,842 ; and \$39,815. The initial investment required

for each respective project: \$628,200 ; \$352,100 ; \$1,245,600 ;

\$814,300 ; \$124,500 ; \$958,000 ; \$2,356,400 ; \$226,900 ;

\$1,650,000 ; and \$714,650. The projects require supervision (A-J:

13, 15, 8, 6, 24, 10, 5, 9, 3, and 11 resource months respectively)

and there are a total of 50 resources months of supervision

available across all of these projects. We are also informed that

projects A, D, and H are mutually exclusive. Which projects

should be selected for action in the current budget cycle?

Tables

SMO production costs (rows are machines, columns are part types)

M-1

M-2

M-3

P-1

3

4

2

P-2

3

1

2

P-3

2

1

5

P-4

5

2

1

P-5

2

2

1

TTA Freight Compartment Specifications

Compartment

Front

Center

Rear

Max Wt (t)

10

16

8

Max Vol (m3)

6800

8700

5300

TTA Available Cargo Specifications

Cargo

1

2

3

4

Wt (t)

18

15

23

12

Vol/t (m3)

480

650

580

390

Profit/t

310

380

350

285

P-6

1

1

2

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