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Exam 23: Linear Programming Models

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Question 41

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A linear programming problem contains a restriction that reads "the quantity of Q must be at least as large as the sum of R,S,and T." Formulate this as a linear programming constraint.

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Q ≥ R + S ...

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Question 42

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

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S ≤ .25 T ...

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Question 43

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What is the feasible region in a linear programming problem?

Which of the following combinations of constraints has no feasible region?

A financial advisor is about to build an investment portfolio for a client who has $100,000 to invest.The four investments available are A,B,C,and D.Investment A will earn 4 percent and has a risk of two "points" per $1,000 invested.B earns 6 percent with 3 risk points;C earns 9 percent with 7 risk points;and D earns 11 percent with a risk of 8.The client has put the following conditions on the investments: A is to be no more than one-half of the total invested.A cannot be less than 20 percent of the total investment.D cannot be less than C.Total risk points must be at or below 1,000. Let A be the amount invested in investment A,and define B,C,and D similarly. Formulate the linear programming model.

Two methods of solving linear programming problems by hand include the corner-point method and the ________.

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

Constraints are needed to solve linear programming problems by hand,but not by computer.

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

In sensitivity analysis,a zero shadow price (or dual value)for a resource ordinarily means that the resource has not been used up.

Explain how to use the iso-profit line in a graphical solution to maximization problem.

A linear programming problem has two constraints 2X + 4Y ≥ 100 and 1X + 8Y ≤ 100,plus nonnegativity constraints on X and Y.Which of the following statements about its feasible region is TRUE?

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.

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

Suppose that a constraint for assembly time has a shadow price of $50/hour for 15 hours in either direction and that all available assembly time is currently used (would require overtime to do more).If the salary of workers is $30 and they receive 50% extra pay for overtime what should management do?

A shadow price (or dual value) reflects which of the following in a maximization problem?

For the constraints given below,which point is in the feasible region of this maximization problem? (1) 14x + 6y ≤ 42 (2) x - y ≤ 3 (3) x,y ≥ 0

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

What is linear programming?

The Queen City Nursery manufactures bags of potting soil from compost and topsoil.Each cubic foot of compost costs 12 cents and contains 4 pounds of sand,3 pounds of clay,and 5 pounds of humus.Each cubic foot of topsoil costs 20 cents and contains 3 pounds of sand,6 pounds of clay,and 12 pounds of humus.Each bag of potting soil must contain at least 12 pounds of sand,at least 12 pounds of clay,and at least 10 pounds of humus.Formulate the problem as a linear program.Plot the constraints and identify the feasible region.Graphically or with corner points find the best combination of compost and topsoil that meets the stated conditions at the lowest cost per bag.Identify the lowest cost possible.