midterm1_Qiong - MidTerm Exam (IE-310) (Monday, Oct 14,...

MidTerm Exam (IE-310)
(Monday, Oct 14, 1:00-1:50pm, open book/notes)
Name:
Total: 60 points.
Problem 1 A farmer specializes in raising grain, corn, and sugar beets on his
5 acres of land. He wants to decide how much land to devote to each crop.
The farmer knows that at least 1 tons (T) of wheat and 2 T of corn are
needed for cattle feed (these needs must be satisfied). Any production in excess
of the feeding requirement would be sold. Selling prices are $200 and $150 per
ton of wheat and corn, respectively. Sugar beet sells at $40 T. The mean yield
on his land is roughly 2T, 3T, and 20T per acre for wheat, corn, and sugar.
1. (6 pt) Formulate a LP to help the farmer to make a plan for the use of
his land to maximize his total income.
2. (2 pt) Formulate the augmented LP.
3. (2pt) Identify basic variables at the initial stage of SIMPLEX iteration.
Identify the entering basic variable and the departing basic variable (through
min ratio test) for the first step of SIMPLEX iteration.