|Topic||Operational Management – Linear Programming|
|Sources / references|
|Description / paper instructions
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.
3y<=4x, 2x+3y<=8, x>=3
2. The constraints on a
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
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 four 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 $100 on each scope, $200 on each pair of
binocs, and $350 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.)
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.
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