Complete Parts I-III

I.  Computer Lab Exercise

Complete (and turn in) the linear programming computer lab exercise.  This will be handed out in class.  We will be going to the computer lab on Friday, June 15 to begin work on this part of the homework.
 

Note: For problems II and III, A,B,C,D are the last four nonzero digits of your social security number
(e.g., 558-56-0900, A=8,B=5,C=6 and D=9)

II. Cost/Revenue Problem

You are given the following revenue (R(X)) and cost (C(X)) functions:
i) R(X)= P*X where P=D*100
ii) C(X)= B*100 - C*X + A*X*X

For example, if A=8, B=5, C=6 and D=9, then R(X)= 900*X and C(X)= 500 - 6*X + 8*X*X
Note P=price and X=production or output.

Using the above functions, complete the following:
a) List A,B,C and D based on your social security number.

b) Prepare a spreadsheet containing the following columns: Production (X), Revenue (R),  Cost (C),
and Profit (R-C). Vary production from 0 to 150 units (by 5 unit increments)

c) Using the graphical capabilities of your spreedsheet (Excel), plot the revenue, cost and profit functions.
Be sure to label the curves and the axes.

d) At what level of production is profit maximized (or losses minimized)? Does a break even point
exist between 0-150 units?  If so, what is the value?

III. Farm Production Problem

     A farmer has a (A00 +1000) acre farm in Carroll County.  The farmer is trying to determine how
many acres of Cotton, Peanuts and Soybeans to plant.  The farmer expects the following profits
per acre for each of the crops:
          Cotton = B00;
          Peanuts = C00;
          Soybeans = D00.

Profit maximization must take into account the following limitations:

          Labor Use cannot exceed ABC + 200 hours;
          Fertilizer use cannot exceed BCD + 250 tons;
          Insecticide use cannot exceed CBA + 300 tons.
          Total acres of farm land available cannot be exceeded;

In addition, the following material requirements must be considered:

Labor hours per acre required are: 1.A for cotton, 1.B for peanuts and 1.C for soybeans;

Tons of fertilizer required per acre are:  1.D for cotton, 1.A for peanuts and 1.B for soybeans;

Tons of insecticide required per acre are: 1.D for cotton, 1.C for peanuts and 1.A for soybeans.

Based on the above, do the following:

a) Write the linear programming model.  Be sure to state the objective function and the constraints.

Using Management Scientist, answer the following:

b) What is the profit maximizing number of acres to plant in cotton, peanuts and soybeans?
Include a copy of the MGT Scientist printout.

c) What is the maximum possible profit?

d) Considering each separately, How much would profits increase
if you were able to obtain an additional:
          i)   200 hours of labor;
          ii)  200 tons of fertilizer;
          iii) 200 tons of insecticide and
          iv) 100 acres of farm land.

Include a printout if the change in the right hand side is "outside the limits."

e) Indicate the impact on the profit level and planting plans if the profit per acre from peanuts were
to increase by $300. Explain why your solution did (or didn't) change.

f) What is the impact on your solution if you force the farmer to plant every acre on his/her farm?
 

Be sure to label your responses and staple your answer sheets in order.