A Business Manager for a Grain Distributor Is Asked to Decide

question 29

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.
​
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?

---

Definitions:

Average Expenditure

The total spending divided by the number of units bought, used to calculate the average cost of goods or services.

Rent Seeking

Spending money in socially unproductive efforts to acquire, maintain, or exercise monopoly.

Monopoly

A market structure characterized by a single seller dominating the entire market, often leading to higher prices due to lack of competition.

Demand Curve

The demand curve is a graph showing the relationship between the price of a good and the amount that consumers are willing and able to purchase at various prices.