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Exam 23: Linear Programming

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Question 41

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What combination of x and y will yield the optimum for this problem? Maximize $3x + $15y,subject to (1) 2x + 4y ≤ 12 and (2) 5x + 2y ≤ 10 and (3) x,y ≥ 0.

A) x = 2,y = 0
B) x = 0,y = 3
C) x = 0,y = 0
D) x = 1,y = 5
E) x = 0,y = 5

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Question 42

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Which of the following is not a requirement of a linear programming problem?

A) an objective function,expressed in linear terms
B) constraints,expressed as linear equations or inequalities
C) an objective function to be maximized or minimized
D) alternative courses of action
E) one constraint or resource limit for each decision variable

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Question 43

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Which of the following represents a valid constraint in linear programming?

In the graphical solution to a linear program,the region that satisfies the constraint 4X + 15Z ≥ 1000 includes the origin of the graph.

Suppose that an iso-profit line is given to be X + Y = 10.Which of the following represents another iso-profit line for the same scenario?

Consider the following constraints from a two-variable linear program:X ≥ 1;Y ≥ 1;X + Y ≤ 9. If these are the only constraints,which of the following points (X,Y) CANNOT be the optimal solution?

What is sensitivity analysis?

A linear programming problem has three constraints,plus nonnegativity constraints on X and Y.The constraints are: 2X + 10Y ≤ 100; 4X + 6Y ≤ 120; 6X + 3Y ≥ 90. What is the largest quantity of X that can be made without violating any of these constraints?

A common form of the product-mix linear programming problem seeks to find that combination of products and the quantity of each that maximizes profit in the presence of limited resources.

For a linear programming problem with the constraints 2X + 4Y ≤ 100 and 1X + 8Y ≤ 100,two of its corner points are (0,0)and (0,25).

A manager must decide on the mix of products to produce for the coming week.Product A requires three minutes per unit for molding,two minutes per unit for painting,and one minute for packing.Product B requires two minutes per unit for molding,four minutes for painting,and three minutes per unit for packing.There will be 600 minutes available for molding,600 minutes for painting,and 420 minutes for packing.Both products have contributions of $1.50 per unit.Answer the following questions; base your work on the solution panel provided. a.What combination of A and B will maximize contribution? b.What is the maximum possible contribution? c.Are any resources not fully used up? Explain.

The feasible region in the diagram below is consistent with which one of the following constraints?

The requirements of linear programming problems include an objective function,the presence of constraints,objective and constraints expressed in linear equalities or inequalities,and ________.

A linear programming problem contains a restriction that reads "the quantity of S must be no less than one-fourth as large as T and U combined." Formulate this as a linear programming constraint.

A firm makes two products,Y and Z.Each unit of Y costs $10 and sells for $40.Each unit of Z costs $5 and sells for $25.If the firm's goal were to maximize profit,what would be the appropriate objective function?

A linear programming problem contains a restriction that reads "the quantity of X must be at least twice as large as the quantity of Y." Formulate this as a linear programming constraint.

________ are restrictions that limit the degree to which a manager can pursue an objective.

What are corner points? What is their relevance to solving linear programming problems?

A difference between minimization and maximization problems is that:

Sensitivity analysis can be applied to linear programming solutions by either (1)trial and error or (2)the analytic postoptimality method.