A business manager for a grain distributor is asked to decide how many containers of each of two grains to purchase to fill its 1,600 pound capacity warehouse. The table below summarizes the container size, availability, and expected profit per container upon distribution.

a. Formulate as a linear program with the decision variables representing the number of containers purchased of each grain. Solve for the optimal solution.
b. What would be the optimal solution if you were not allowed to purchase fractional containers?
c. There are three possible results from rounding an LP solution to obtain an integer solution:
(1) the rounded optimal LP solution will be the optimal IP solution;
(2) the rounded optimal LP solution gives a feasible, but not optimal IP solution;
(3) the rounded optimal LP solution is an infeasible IP solution.

For this problem (i) round down all fractions; (ii) round up all fractions; (iii) round off (to the nearest integer) all fractions (NOTE: Two of these are equivalent.) Which result above (1, 2, or 3) occurred under each rounding method?

Question

A business manager for a grain distributor is asked to decide how many containers of each of two grains to purchase to fill its 1,600 pound capacity warehouse. The table below summarizes the container size, availability, and expected profit per container upon distribution.
​  ​ 
a. Formulate as a linear program with the decision variables representing the number of containers purchased of each grain. Solve for the optimal solution.
b. What would be the optimal solution if you were not allowed to purchase fractional containers?
c. There are three possible results from rounding an LP solution to obtain an integer solution:
(1) the rounded optimal LP solution will be the optimal IP solution;
(2) the rounded optimal LP solution gives a feasible, but not optimal IP solution;
(3) the rounded optimal LP solution is an infeasible IP solution.
​
For this problem (i) round down all fractions; (ii) round up all fractions; (iii) round off (to the nearest integer) all fractions (NOTE: Two of these are equivalent.) Which result above (1, 2, or 3) occurred under each rounding method?

Quizplus · Accepted Answer

The Answer of A business manager for a grain distributor is asked to decide how many containers of each of two grains to purchase to fill its 1,600 pound capacity warehouse. The table below summarizes the container size, availability, and expected profit per container upon distribution.
​  ​ 
a. Formulate as a linear program with the decision variables representing the number of containers purchased of each grain. Solve for the optimal solution.
b. What would be the optimal solution if you were not allowed to purchase fractional containers?
c. There are three possible results from rounding an LP solution to obtain an integer solution:
(1) the rounded optimal LP solution will be the optimal IP solution;
(2) the rounded optimal LP solution gives a feasible, but not optimal IP solution;
(3) the rounded optimal LP solution is an infeasible IP solution.
​
For this problem (i) round down all fractions; (ii) round up all fractions; (iii) round off (to the nearest integer) all fractions (NOTE: Two of these are equivalent.) Which result above (1, 2, or 3) occurred under each rounding method?

A Business Manager for a Grain Distributor Is Asked to Decide