Answer to Question #288773 in Management for Achini Eranga

Question

1.      A farmer has 1000 perches of land in which he can grow corn, millet, or cowpea. Each perch of corn costs Rs 100/- for preparation, requires 7 man-days of work and yields a profit of Rs 30/-. A perch of millet costs Rs 120/- for preparation, requires 10 man-days of work and yields a profit of Rs 40/-. A perch of cowpea costs Rs 70/- for preparation, requires 8 man-days of work and yields a profit of Rs 20/-. The farmer has Rs 100,000/- for preparation and can count on 8,000 man-days work.

a.      Formulate a linear programming model for the above problem. (Use X1, X2 and X3 for corn, millet, and cowpea respectively).                                  (5 marks)

b.      Prepare the first simplex table.                              (2 marks)

c.      Find the pivot element.                                    (2 marks)

Answer 1

x acres for corn;

y acres for wheat;

z acres for soybeans.


The profit function

P(x,y,z) = 30x + 20y + 20z            (1)    (= objective function)



Restrictions:

x   +     y +   z <= 1000             (2)   (1000 acres in all)

100x + 120y + 70z <= 100000           (3)   (cost for preparation)

7x   +  10y +  8z <= 8000             (4)   (man-days work)

x >= 0,  y >= 0,  z >=  0             (5)   (standard non-negativity restrictions)

The Answer is   X = 1000 acres;  Y = 0 acres;  Z = 0 acres;  p = 30000.