Exam 23: Linear Programming Models

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 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 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?

Using the iso-profit line solution method to solve a maximization problem requires that we:

For the following constraints,which point is in the feasible region of this minimization problem? (1)14x + 6y > 42 (2)x - y > 3

What are the requirements of all linear programming problems?

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.

A feedlot is trying to decide on the lowest cost mix that will still provide adequate nutrition for its cattle.Suppose that the numbers in the chart represent the number of grams of ingredient per 100 grams of feed and that the cost of Feed X is $5/100grams,Feed Y is $3/100 grams,and Feed X is $8/100 grams.Each cow will need 50 grams of A per day,20 grams of B,30 grams of C,and 10 grams of D.The feedlot can get no more than 200 grams per day per cow of any of the feed types.Formulate the problem as a linear program.

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

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 maximizing linear programming problem has two constraints: 2X + 4Y ≤ 100 and 3X + 10Y ≤ 210,in addition to constraints stating that both X and Y must be nonnegative.What are the corner points of the feasible region of this problem?

What is the simplex method?

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).

The diet problem is known in agricultural applications as the:

Solving a linear programming problem with the iso-profit line solution method requires that we move the iso-profit line to each corner of the feasible region until the optimum is identified.

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

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. a.Algebraically state the objective and constraints of this problem. b.Plot the constraints on the grid below and identify the feasible region.

In which of the following has LP been applied successfully?

An iso-profit line: