1. Make a sketch of the feasibility region defined by the following
constraints. Label the edges of the region with numbers; label the
extrema with letters. Find and present the coordinates of the
extrema. Assume that x and y are both equal to or greater than
zero.
Version B: 2y<=2x, 2x+3y<=15, 3y>=x, x>=1
2. The constraints
on a particular
manufacturing
process are shown
on the right. The
extrema of the
feasibility region
have been
calculated and
plotted.
Using the profit
function given
below, calculate
the profit (value of
P) at each
extrema.
P=x+2y
At which extremum
is the profit the
maximum? The
minimum? (A
negative profit is a
loss. The minimum
profit is either the
smallest positive
profit, or the largest
loss.)
3. Eye-Full Optics assembles astronomical telescopes (x), premium
binoculars (y) and student-grade microscopes (z) from imported
parts. Each telescope takes one hour to assemble, each pair of
binoculars two hours, and each microscope three hours; the
availability of skilled labor limits assembly work to 1000 hours per
day. Eye-Full has a contract with FedEx, and must ship no less than
400 items per day. A contract with a major retailer requires them to
deliver a minimum of 100 telescopes, 250 binocs, and 50
microscopes per day. But there are supply limitations. The
telescopes and binocs are shipped with the same eyepieces; each
scope has one, and each pair of binocs has two. The subcontractor
who supplies the eyepieces can only furnish 800 per day. Similarly,
both the binocs and the microscopes use the same prisms; each
pair of binocs needs two, and each microscope needs four. The
prism supplier can only ship Eye-Full 1600 per day.
If Eye-Full makes a profit on $150 on each scope, $220 on each
pair of binocs, and $300 on each microscope, how many of each
should the company manufacture each day? What is its daily profit?
(Since the feasibility region is a volume in three-dimensional space,
a sketch is not required.)
(HINT: Use an online app to solve Problem 3. Submit a screen shot
of the output, plus an explanation.)
Please read and heed the hints given in Cases 1, 2, and 3. The
same general advice is applicable in this Case, in particular:
1. Read the source materials before beginning.
2. The Case is about linear programming, not the wider topic of
production planning.
3. Follow standard format. A cover page, a short discussion, references
and citations are all required.
4. In case you missed it: Use an application to work out Problem 3.
Insert a screen shot of the output. Be sure to provide a reference and
a citation for the app you use.
Assignment Expectations
Graphics must be neat, clear and complete. A graphics app can be
used, but a freehand sketch is also acceptable.
All calculations should be shown.
All answers must be clearly stated.
Relevant theory should be cited as necessary to explain which
procedures were used to arrive at the answers, and why.
Follow the instructions in the BSBA Writing Style Guide (July 2014
edition), available online at https://mytlc.trident.edu/files/WritingGuide_Trident_2014.pdf.
There are no guidelines concerning length. Write what you need to
write – neither more, nor less.
Clearly demonstrate your understanding of both the theory covered in
the Module, and the particulars of the Case.
Provide references and citations. At a minimum, you should reference
the course materials. These are referenced in APA format on the
Background Info page.
