1.What does LPP stand for?
2.The linear function $Z = ax + by$ which is to be maximized or minimized is called the ________ function.
3.The variables $x$ and $y$ whose values we need to determine in an LPP are called ________ variables.
4.The conditions $x \ge 0, y \ge 0$ in an LPP are specifically called ________ restrictions.
5.The common region determined by all the constraints, including non-negative constraints, is called the ________ region.
6.Any point inside or on the boundary of the feasible region represents a ________ solution.
7.A solution in the feasible region that produces the maximum or minimum value of the objective function is called an ________ solution.
8.Points outside the feasible region represent ________ solutions.
9.True or False: The feasible region of a standard LPP is always a convex set.
10.True or False: In a Linear Programming Problem, the objective function and all constraints must be linear.
11.In a "Diet problem", what is usually our objective regarding the cost of the diet? (Maximize or Minimize)
12.In a "Manufacturing problem", what is usually our objective regarding the profit? (Maximize or Minimize)
13.If a machine has "at most" $10$ hours of time available, which mathematical symbol is used for this constraint? ($\le$, $\ge$, or $=$)
14.If a diet requires "at least" $20$ units of vitamin A, which mathematical symbol is used for this constraint? ($\le$, $\ge$, or $=$)
15.If the total transportation cost is given by $Z = 50x + 60y$, is this equation an objective function or a constraint?
16.The Corner Point Theorem states that the optimal value of the objective function must occur at a ________ of the feasible region.
17.If the feasible region can be entirely enclosed within a circle, it is called a ________ region.
18.If the feasible region extends indefinitely in some direction and cannot be enclosed in a circle, it is called an ________ region.
19.For a bounded feasible region, do both maximum and minimum values of the objective function $Z$ always exist? (Yes or No)
20.For an unbounded region, if $M$ is the maximum value at a corner point, we must draw a dotted line for $ax + by$ ________ $M$ to check if a larger value exists. (Fill with $>$ or $<$)
21.For an unbounded region, if $m$ is the minimum value at a corner point, we must draw a dotted line for $ax + by$ ________ $m$ to verify the minimum. (Fill with $>$ or $<$)
22.What is the value of the objective function $Z = 3x + 4y$ at the corner point $(0, 5)$?
23.What is the value of the objective function $Z = 5x + 2y$ at the corner point $(4, 0)$?
24.If the optimal value occurs at exactly one corner point, the LPP is said to have a ________ optimal solution.
25.If the maximum value of $Z$ occurs at two adjacent corner points, how many optimal solutions does the LPP have?
26.In the case of multiple optimal solutions (from Q25), where do all these optimal solutions geometrically lie?
27.If the constraints of an LPP are mutually contradictory (resulting in no common region), the LPP has an ________ solution (or no feasible solution).
28.True or False: An LPP can have exactly two optimal solutions.
29.The straight line $ax + by = k$ representing a constant profit value $k$ is known as an ________ line.
30.True or False: All Iso-profit lines for a given objective function $Z = ax + by$ are parallel to each other.
