Exam 23: Linear Programming

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.

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.

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?

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

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

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.

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

One requirement of a linear programming problem is that the objective function must be expressed as a linear equation.

What is the usefulness of a shadow price (or dual value)?

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?

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

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?

The graphical method of solving linear programs can handle only maximization problems.

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

A linear programming problem contains a restriction that reads "the quantity of Q must be no larger than the sum of R,S,and T." Formulate this as a linear programming constraint.

The objective of a linear programming problem is to maximize 1.50A + 1.50B,subject to 3A + 2B ≤ 600,2A + 4B ≤ 600,1A + 3B ≤ 420,and A,B ≥ 0. a.Plot the constraints on the grid below c.Identify the feasible region and its corner points.Show your work. d.What is the optimal product mix for this problem?

The property manager of a city government issues chairs,desks,and other office furniture to city buildings from a centralized distribution center.Like most government agencies,it operates to minimize its costs of operations.In this distribution center,there are two types of standard office chairs,Model A and Model B.Model A is considerably heavier than Model B,and costs $20 per chair to transport to any city building;each model B costs $14 to transport.The distribution center has on hand 400 chairs-200 each of A and B. The requirements for shipments to each of the city's buildings are as follows: Building 1 needs at least 100 of A Building 2 needs at least 150 of B. Building 3 needs at least 100 chairs,but they can be of either type,mixed. Building 4 needs 40 chairs,but at least as many B as A. Formulate this problem as a linear program.(Hint: there are eight decision variables because we need to know how many of each chair (A and B)to deliver to each of the four buildings).

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

Rienzi Farms grows sugar cane and soybeans on its 500 acres of land.An acre of soybeans brings a $1000 contribution to overhead and profit;an acre of sugar cane has a contribution of $2000.Because of a government program no more than 200 acres may be planted in soybeans.During the planting season 1200 hours of planting time will be available.Each acre of soybeans requires 2 hours,while each acre of sugar cane requires 5 hours.The company seeks maximum contribution (profit)from its planting decision. a.Formulate the problem as a linear program. b.Solve using the corner-point method.

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.