A Business Manager for a Grain Distributor Is Asked to Decide

question 58

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. $\begin{array}{cccc} & \text { Container } & \text { Containers } & \text { Container } \\\text { Grain } & \text { Size } & \text { Available } & \text { Profit } \\\hline \text { A } & 500 \mathrm{lbs} & 3 & \$ 1,200 \\\text { B } & 600 \mathrm{lbs} & 2 & \$ 1,500\end{array}$
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?

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Definitions:

Legal Processes

Formal procedures and practices followed in the administration of justice, including litigation and judicial decisions.

Financing Statement

A document filed to give public notice to third parties of a security interest in personal property.

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Specialized language used in the field of law, encompassing terms, phrases, and principles pertinent to legal proceedings and documentation.

Real Property

Refers to land and anything permanently attached to it, such as buildings and structures, legally considered immovable.