Question Details

MAT 540
WEEK 7
1) Linear programming is a model consisting of linear relationships representing a firm's 
decisions given an objective and resource constraints. 
2) The objective function is a linear relationship reflecting the objective of an operation. 
Answer:  TRUE
3) A constraint is a linear relationship representing a restriction on decision making. 
4) A linear programming model consists of only decision variables and constraints.
5) A feasible solution violates at least one of the constraints. 
6) Proportionality means the slope of a constraint is proportional to the slope of the objective 
function. 
7) The terms in the objective function or constraints are additive. 
8) The terms in the objective function or constraints are multiplicative. 
9) The values of decision variables are continuous or divisible. 
Answer:  TRUE
10) All model parameters are assumed to be known with certainty. 
11) In linear programming models , objective functions can only be maximized. 
12) All linear programming models exhibit a set of constraints. 
13) Linear programming models exhibit linearity among all constraint relationships and the 
Answer:  FALSE
14) The equation 8xy = 32 satisfies the proportionality property of linear programming. 
15) Objective functions in linear programs always minimize costs. 
Answer:  TRUE
16) The feasible solution area contains infinite solutions to the linear program. 
17) There is exactly one optimal solution point to a linear program. 
18) The following equation represents a resource constraint for a maximization problem: X + Y 
19) A minimization model of a linear program contains only surplus variables.
20) In the graphical approach, simultaneous equations may be used to solve for the optimal 
21) Slack variables are only associated with maximization problems. 
22) Surplus variables are only associated with minimization problems. 
23) If the objective function is parallel to a constraint, the constraint is infeasible.
Answer:  FALSE
24) Multiple optimal solutions occur when constraints are parallel to each other.
25) Graphical solutions to linear programming problems have an infinite number of possible 
objective function lines. 
26) The first step in formulating a linear programming model is to define the objective function.
27) __________ are mathematical symbols representing levels of activity. 
28) The __________ is a linear relationship reflecting the objective of an operation. 
Answer:  constraint 
29) A __________ is a linear relationship representing a restriction on decision making. 
30) If at least one constraint in a linear programming model is violated the solution is said to be  
Answer:  infeasible 
__________. 
decision variables 
31) A graphical solution is limited to solving linear programming problems with __________ 
Answer:  feasible 
32) The __________ solution area is an area bounded by the constraint equations. 
constraint line. 
33) Multiple optimal solutions can occur when the objective function line is __________ to a 
34) When a maximization problem is __________, the objective function can increase 
indefinitely without reaching a maximum value. 
35) A linear programming problem that results in a solution that is __________ usually indicates 
that the linear program has been incorrectly formulated. 
36) In a constraint the __________ variable represents unused resources. 
37) If the objective function is parallel to a constraint, the linear program could have 
__________. 
38) Corner points on the boundary of the feasible solution area are called __________ points.
39) The __________ step in formulating a linear programming model is to define the decision 
variables.
40) The __________ property of linear programming models indicates that the values of all the 
Answer:  certainty 
model parameters are known and are assumed to be constant. 
41) The __________ property of linear programming models indicates that the rate of change or 
slope of the objective function or a constraint is constant. 
42) The __________ property of linear programming models indicates that the decision variables 
cannot be restricted to integer values and can take on any fractional value. 
43) The constraint, 2X +XY violates the __________ property of linear programming. 
44) Consider the following minimization problem: 
Min z = 	x1 + 2x2 
s.t. 	x1 + x2 ≥ 300 
	2x1 + x2 ≥ 400 
	2x1 + 5x2 ≤ 750 
	x1, x2 ≥ 0 
What is the optimal solution?