Question 1 Check the statements below which are true. It\'s not easy to get the
ID: 3167978 • Letter: Q
Question
Question 1 Check the statements below which are true. It's not easy to get the truth or falsity of all of these statements correct the first time. You'll probably want to discuss some of the questions in person or on piazza with your colleagues. A. Every feasible solution is in the domain of the objective function B. Maximums of linear functions occur at points where the gradient is zero. - C. A feasible basic solution is a corner point of the domain of the objective function. D. Every basic solution lies in the domain of the objective function. E. A basic solution is a point determined by the intersection of enough hyperplanes F. A basic solution with 5 zeros lies on 5 hyperplanes G. Every point in the domain of the objective function is a feasible solution H. The gradient of a linear function is constant. I. Strict maximums of linear functions on closed sets always occur on the boundaryExplanation / Answer
a.
Domain is the set of values for which a function is defined.
The optimization technique aims to find best values for an objective function i.e. the feasible values comes in the boundaries of the objective function. All the feasible values are derived from corner points of the common region which satisfies the objective function.
Thus, statement A is correct.
b.
f(x) = ax + b
where a = gradient
b = y-axis intercept / vertical intercept.
If the value of x will be taken as zero, then the resultant will be very nominal. But if there is some value assigned to x, the value of linear function will increase as many time equal to x.
Therefore, it is not right to say that maximus of linear functions occur at points where gradient is zero.
Hence, statement B is false.
c.
Feasible solution is derived by substituting the value of corner points in the objective function. Since the corner points comes in domain of the objective function, it would be right to say that statement C is true.
d.
A basic solution is the one which satisfies all the conditions of a problem. In linear problems, we tend to seek basic feasible solution instead of basic solution to satisfy the objective function.
Hence, the given statement is false.
e.
A basic solution is arrived at by the corner points which are determined by the intersection of various hyperplanes. Thus, the statement is true.
f.
The statement is true because the number of hyperplanes is equal to the number of number of zeroes i.e. linear equations.
g.
Every point in the domain of objective function is feasible solution but not the optimal solution. Therefore, the statement is true.
h.
The graph of a linear function is straight line. Thus, the slope is always constant. Hence, the statement is true.
i.
The maximum value of a linear function is always obtained on the boundary points. Thus, the statement is true.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.