Exam 7: Introduction to Linear Programming

Consider the following linear program: MAX 60X + 43Y s.t.X + 3Y > 9 6X -0 2Y = 12 X + 2Y < 10 X,Y > 0 a.Write the problem in standard form. b.What is the feasible region for the problem? c.Show that regardless of the values of the actual objective function coefficients,the optimal solution will occur at one of two points.Solve for these points and then determine which one maximizes the current objective function.

For the following linear programming problem,determine the optimal solution by the graphical solution method Max -X + 2Y s.t.6X - 2Y $\le$ 3 -2X + 3Y - 6 X + Y $\le$ 3 X,Y $\ge$ 0

All of the following statements about a redundant constraint are correct EXCEPT

Solve the following linear program graphically. MAX 5X + 7Y s.t.X < 6 2X + 3Y < 19 X + Y < 8 X,Y > 0

As long as the slope of the objective function stays between the slopes of the binding constraints

A solution that satisfies all the constraints of a linear programming problem except the nonnegativity constraints is called

The improvement in the value of the objective function per unit increase in a right-hand side is the

Solve the following system of simultaneous equations. 6X + 2Y = 50 2X + 4Y = 20

Because surplus variables represent the amount by which the solution exceeds a minimum target,they are given positive coefficients in the objective function.

The constraint 2x₁ - x₂ = 0 passes through the point (200,100).

An unbounded feasible region might not result in an unbounded solution for a minimization or maximization problem.

A businessman is considering opening a small specialized trucking firm.To make the firm profitable,it is estimated that it must have a daily trucking capacity of at least 84,000 cu.ft.Two types of trucks are appropriate for the specialized operation.Their characteristics and costs are summarized in the table below.Note that truck 2 requires 3 drivers for long haul trips.There are 41 potential drivers available and there are facilities for at most 40 trucks.The businessman's objective is to minimize the total cost outlay for trucks. Solve the problem graphically and note there are alternate optimal solutions.Which optimal solution: a.uses only one type of truck? b.utilizes the minimum total number of trucks? c.uses the same number of small and large trucks?

Solve the following linear program by the graphical method. MAX 4X + 5Y s.t.X + 3Y < 22 -X + Y < 4 Y < 6 2X - 5Y < 0 X,Y > 0

Find the complete optimal solution to this linear programming problem. Min 5X + 6Y s.t.3X + Y > 15 X + 2Y > 12 3X + 2Y > 24 X ,Y > 0

An optimal solution to a linear programming problem can be found at an extreme point of the feasible region for the problem.

Because the dual price represents the improvement in the value of the optimal solution per unit increase in right-hand-side,a dual price cannot be negative.

A range of optimality is applicable only if the other coefficient remains at its original value.

Find the complete optimal solution to this linear programming problem. Max 2X + 3Y s.t.4X + 9Y < 72 10X + 11Y < 110 17X + 9Y < 153 X ,Y > 0

Given the following linear program: MIN 150X + 210Y s.t.3.8X + 1.2Y > 22.8 Y > 6 Y < 15 45X + 30Y = 630 X,Y > 0 Solve the problem graphically.How many extreme points exist for this problem?

The Sanders Garden Shop mixes two types of grass seed into a blend.Each type of grass has been rated (per pound)according to its shade tolerance,ability to stand up to traffic,and drought resistance,as shown in the table.Type A seed costs $1 and Type B seed costs $2.If the blend needs to score at least 300 points for shade tolerance,400 points for traffic resistance,and 750 points for drought resistance,how many pounds of each seed should be in the blend? Which targets will be exceeded? How much will the blend cost?