A Business Manager for a Grain Distributor Is Asked to Decide

question 13

Essay

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.
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For this problem,(i)round down all fractions; (ii)round up all fractions; and (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?

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Definitions:

Percent Rate

a rate that describes a portion of a hundred in finance, often related to interest or growth rates.

Portion

A part or segment of the whole, often expressed as a fraction or percentage.

Accurate

Describes information, measurements, or results that are exact, precise, and free from errors or mistakes.

Cent

A monetary unit equal to one hundredth of a larger unit, such as a dollar or euro.