Asked by Ethan Belka on Jun 28, 2024
Verified
Which of the following explains the capacity constraint for the Kansas plant?
A) X41 + X42 + X43 + X44 ≤ 3,000Y1
B) X41 + X42 + X43 + X44 ≤ 3,000Y2
C) X41 + X42 + X43 + X44 ≤ 3,600
D) X41 + X42 + X43 + X44 ≤ 1,400
Capacity Constraint
A limitation on the resources available for production, such as time, labor, or materials, which can affect the maximum output levels.
Double-subscripted Variables
Variables in mathematical modeling that are indexed by two sets, often used to represent the elements in a matrix or a two-dimensional array.
- Apply binary variable utilization in decision-making for optimal solutions.
- Understand the factors influencing the strategic expansion of manufacturing capacity, including location analysis.
Verified Answer
WL
Wesly LaguerreJul 03, 2024
Final Answer :
B
Explanation :
The capacity constraint for the Kansas plant is given by the inequality X41 + X42 + X43 + X44 ≤ 3,000Y2, which states that the total amount shipped from the Kansas plant to all distribution centers cannot exceed 3,000 units if the Kansas plant is built.
To determine the best choice, we need to compare the total transportation cost for each option. We can compute the total cost for building the Ohio plant by multiplying the unit cost of each route by the corresponding amount shipped and summing over all routes. Similarly, we can compute the total cost for building the Kansas plant. The plant that results in the lower total cost is the best choice.
To determine the best choice, we need to compare the total transportation cost for each option. We can compute the total cost for building the Ohio plant by multiplying the unit cost of each route by the corresponding amount shipped and summing over all routes. Similarly, we can compute the total cost for building the Kansas plant. The plant that results in the lower total cost is the best choice.
Learning Objectives
- Apply binary variable utilization in decision-making for optimal solutions.
- Understand the factors influencing the strategic expansion of manufacturing capacity, including location analysis.
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