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Questions and Answers
In the given objective function $Z = 10x_A + 15x_B + 2x_A + 3x_B + 5I + 4D$, which term represents the cost associated with product B?
In the given objective function $Z = 10x_A + 15x_B + 2x_A + 3x_B + 5I + 4D$, which term represents the cost associated with product B?
- $15x_B + 3x_B$ (correct)
- $10x_A$
- $5I + 4D$
- $2x_A$
A production problem has a labor constraint of $0.5x_1 + 0.3x_2 \leq 500$. If the optimal solution uses 400 labor hours, what can be said about this constraint?
A production problem has a labor constraint of $0.5x_1 + 0.3x_2 \leq 500$. If the optimal solution uses 400 labor hours, what can be said about this constraint?
- It is not binding because the left-hand side does not equal the right-hand side.
- It is binding because all labor hours are not used.
- It is binding because the left-hand side is less than the right-hand side.
- It is not binding because 400 < 500. (correct)
Which of the following variable values satisfies the constraint $3x_1 + 5x_2 \leq 15$, given that $x_1, x_2 \geq 0$?
Which of the following variable values satisfies the constraint $3x_1 + 5x_2 \leq 15$, given that $x_1, x_2 \geq 0$?
- $x_1 = 1, x_2 = 2$ (correct)
- $x_1 = 2, x_2 = 2$
- $x_1 = 3, x_2 = 2$
- $x_1 = 4, x_2 = 1$
A machine capacity constraint is given by: $2x_1 + 3x_2 \leq 600$. If the shadow price for this constraint is 8, what does this imply?
A machine capacity constraint is given by: $2x_1 + 3x_2 \leq 600$. If the shadow price for this constraint is 8, what does this imply?
A manufacturing plant produces two types of products, $P_1$ and $P_2$. Each unit of $P_1$ requires 3 labor hours and each unit of $P_2$ requires 2 labor hours. Given a total of 600 available labor hours, what does the constraint $3x_1 + 2x_2 \leq 600$ represent?
A manufacturing plant produces two types of products, $P_1$ and $P_2$. Each unit of $P_1$ requires 3 labor hours and each unit of $P_2$ requires 2 labor hours. Given a total of 600 available labor hours, what does the constraint $3x_1 + 2x_2 \leq 600$ represent?
A company has two factories and three warehouses. Factory 1 can supply 100 units and Factory 2 can supply 200 units. Warehouses 1, 2, and 3, demand 120, 100, and 80 units, respectively. Which represents the correct demand constraint for Warehouse 2?
A company has two factories and three warehouses. Factory 1 can supply 100 units and Factory 2 can supply 200 units. Warehouses 1, 2, and 3, demand 120, 100, and 80 units, respectively. Which represents the correct demand constraint for Warehouse 2?
In a transportation model, the constraint $x_{11} + x_{21} \geq 400$ is specified. What does $x_{11}$ and $x_{21}$ specifically represent?
In a transportation model, the constraint $x_{11} + x_{21} \geq 400$ is specified. What does $x_{11}$ and $x_{21}$ specifically represent?
In a transshipment model, a constraint is given as $x_{in} + x_{jn} = x_{nk} + x_{nl}$. What does this constraint ensure at a warehouse node represented by $n$?
In a transshipment model, a constraint is given as $x_{in} + x_{jn} = x_{nk} + x_{nl}$. What does this constraint ensure at a warehouse node represented by $n$?
A company makes products A and B, with unit costs of $10 and $15, respectively. Inventory holding costs are $2/unit for A and $3/unit for B. Increased production cost is $5/unit, and a decrease cost is $4/unit. What's the appropriate objective function to minimize total costs?
A company makes products A and B, with unit costs of $10 and $15, respectively. Inventory holding costs are $2/unit for A and $3/unit for B. Increased production cost is $5/unit, and a decrease cost is $4/unit. What's the appropriate objective function to minimize total costs?
For a blending problem where material A must be at least 30% of the total blend, with $x_A$ representing the amount of material A and $x_B$ representing the amount of material B, what is the correct mathematical constraint?
For a blending problem where material A must be at least 30% of the total blend, with $x_A$ representing the amount of material A and $x_B$ representing the amount of material B, what is the correct mathematical constraint?
In a linear programming problem, what occurs if a constraint line is parallel to the objective function?
In a linear programming problem, what occurs if a constraint line is parallel to the objective function?
Consider a feasible region determined by linear constraints. If a line representing a constraint is moved parallel outward (away from the origin) in a maximization problem to the point it no longer contains any points of the feasible region, which of the following is true?
Consider a feasible region determined by linear constraints. If a line representing a constraint is moved parallel outward (away from the origin) in a maximization problem to the point it no longer contains any points of the feasible region, which of the following is true?
A transportation problem involves three supply points (S1, S2, S3) and four demand points (D1, D2, D3, D4). Which of the following correctly sums the flow into demand point D3?
A transportation problem involves three supply points (S1, S2, S3) and four demand points (D1, D2, D3, D4). Which of the following correctly sums the flow into demand point D3?
In production planning, what does a zero inventory level at the end of a planning horizon indicate?
In production planning, what does a zero inventory level at the end of a planning horizon indicate?
In a situation where a decision variable represents the number of units to produce, which of the following is always true in mathematical programming?
In a situation where a decision variable represents the number of units to produce, which of the following is always true in mathematical programming?
During what time is the production quantity in a period is determined in a rolling horizon approach?
During what time is the production quantity in a period is determined in a rolling horizon approach?
Flashcards
What are the components of the total production cost?
What are the components of the total production cost?
The total cost of production includes the cost of manufacturing, inventory holding, and changes in production.
What's a feasible solution in linear programming?
What's a feasible solution in linear programming?
A feasible solution satisfies all the constraints of a linear programming problem.
What does the constraint 3x1 + 2x2 ≤ 600 represent in a production problem?
What does the constraint 3x1 + 2x2 ≤ 600 represent in a production problem?
The constraint represents the maximum number of labor hours available for production.
What does the constraint x11 + x21 ≥ 400 ensure in a transportation problem?
What does the constraint x11 + x21 ≥ 400 ensure in a transportation problem?
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What does the constraint xin + xjn = xnk + xnl enforce in a transshipment problem?
What does the constraint xin + xjn = xnk + xnl enforce in a transshipment problem?
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What does the constraint xA ≥ 0.3(xA + xB) ensure in a blending problem?
What does the constraint xA ≥ 0.3(xA + xB) ensure in a blending problem?
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What does the objective function in a production problem do?
What does the objective function in a production problem do?
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What is a feasibility check?
What is a feasibility check?
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Binding Constraint
Binding Constraint
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Shadow Price
Shadow Price
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Demand Constraint in Transportation
Demand Constraint in Transportation
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Objective Function in Production Planning
Objective Function in Production Planning
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Production Cost
Production Cost
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Inventory Holding Cost
Inventory Holding Cost
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Production Adjustment Cost
Production Adjustment Cost
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Production Increase Cost
Production Increase Cost
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Study Notes
Linear Programming Multiple Choice Questions
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Binding Constraint: A constraint is binding if all available resources are fully utilized in the optimal solution. A constraint is not binding if the optimal solution uses less of the resource than is available.
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Shadow Price: The shadow price for a constraint represents the increase in the objective function value for each unit increase in the resource. In the example, increasing machine capacity by one unit increases total profit by $8.
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Transportation Problem Formulation: Constraints in a transportation problem specify the supply from factories and demand at warehouses. The sum of shipments to a given warehouse equals its demand.
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Objective Function for Production Planning: An objective function calculates the total cost for production, considering variable costs, inventory holding costs, and changes in production.
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Feasibility Check: A solution is feasible if it satisfies all constraints in the linear programming problem. Check the constraint to see if it's mathematically true with the provided values, (e.g. x1 = 1, x2 = 3).
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Production Constraints: Constraints in a production environment specify resource limits. In the example, labor hours (e.g. 600) are used to set limits on combined units produced.
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Demand Fulfillment in Transportation: The constraint ensures a minimum amount of units are shipped from one location to another location.
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Transshipment Problem: The constraint in a transshipment problem ensures that shipments into a warehouse equal shipments out of that warehouse. This is about flow balance.
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Blending Problem Constraints: Ensuring a minimum percentage of a material in a blend requires the correct mathematical constraint. This example implies that material A should be at lease 30% of the total mix.
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Objective Function in Transportation: Objective functions in a transportation problem calculate the total costs of shipping goods; in this example, it considers different shipping costs based on the shipping source and destination.
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