A company has facilitated for producing 5 products which require the same raw material and
the same type of production, finishing and packaging facilities. The unit contribution margin
and the material and labor requirements for each of the products are given here.
PRODUCT CONTRIBUTION
MARGIN
RAW
MATERIAL
(KG)
LABOR HOURS
PRODUCTION
LABOR HOURS
FINISHING &
PRODUCTION
P1 150 10 10 30
P2 120 10 20 20
P3 160 20 10 20
P4 160 30 10 20
P5 100 20 20 10
TOTAL
AVAILABLE
(000)
50 80 140
The manager of the company insists that the products P3 and P4 should be given top priority in
the production, because they yield the maximum contribution.
a) Formulate the above problem as a linear programing model
b) Obtain optimal solution to the problem and state whether you agree with the managers
viewpoint (use the simplex method)
c) Write the dual of this problem
d) Obtain the marginal profitability of (i) raw materials, (ii) the time in the production
department, and (iii) the time in the finishing and packaging department
e) Over what range of values of the respective constraints the marginal profitability
determined by you in (b) earlier would be valid?
f) Verify that the objective function values of the primal and the dual problems are identical.
g) The marketing manager informs that the selling price of the product P2 has to be revised
downward to birr 116. What will be the new optimal product mix and the profit at it?