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OPRE 3333 (Johnston)
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
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?
SMO production costs (rows are machines, columns are part types)
TTA Freight Compartment Specifications
Max Wt (t)
Max Vol (m3)
TTA Available Cargo Specifications
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