Operational Management – Linear Programming

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Case Assignment

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

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=3x-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 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

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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.)

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.