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. Grain s.t. A B Container Size Containers Available Container Profit 500 lbs warehouse capacity 600 lbs available grain containers (a) Formulate a linear program to maximize profit (in dollars) with the decision variables representing the number of containers purchased of each grain, allowing for fractional containers. (Let A be the number of containers of grain A and B be the number of containers of grain B.) Max available grain containers 3 A, B 20 Solve for the optimal solution. (A, B)= 2 $1,100 $1,800 (b) What would be the optimal solution if you were not allowed to purchase fractional containers? (A, B) = (c) There are three possible results from rounding an LP relaxation solution to obtain an integer solution: 1. The rounded optimal LP relaxation solution will be the optimal solution. 2. The rounded optimal LP relaxation solution gives a feasible but not optimal IP solution. 3. The rounded optimal LP relaxation solution is an infeasible IP solution.
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. Grain s.t. A B Container Size Containers Available Container Profit 500 lbs warehouse capacity 600 lbs available grain containers (a) Formulate a linear program to maximize profit (in dollars) with the decision variables representing the number of containers purchased of each grain, allowing for fractional containers. (Let A be the number of containers of grain A and B be the number of containers of grain B.) Max available grain containers 3 A, B 20 Solve for the optimal solution. (A, B)= 2 $1,100 $1,800 (b) What would be the optimal solution if you were not allowed to purchase fractional containers? (A, B) = (c) There are three possible results from rounding an LP relaxation solution to obtain an integer solution: 1. The rounded optimal LP relaxation solution will be the optimal solution. 2. The rounded optimal LP relaxation solution gives a feasible but not optimal IP solution. 3. The rounded optimal LP relaxation solution is an infeasible IP solution.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
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Transcribed Image Text: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.
Max
Grain
s.t.
A
B
Container Size Containers Available
warehouse capacity
(A, B) =
500 lbs
600 lbs
available grain A containers
(A, B) =
(a) Formulate a linear program to maximize profit (in dollars) with the decision variables representing the number of containers purchased of each grain, allowing for fractional containers. (Let A be the number of containers of grain A and B be the number of
containers of grain B.)
available grain B containers
A, B ≥ 0
Solve for the optimal solution.
3
2
Container Profit
$1,100
$1,800
(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 relaxation solution to obtain an integer solution:
1. The rounded optimal LP relaxation solution will be the optimal IP solution.
2. The rounded optimal LP relaxation solution gives a feasible but not optimal IP solution.
3. The rounded optimal LP relaxation solution is an infeasible IP solution.
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