CBSE Questions for Class 12 Commerce Maths Linear Programming Quiz 2 - MCQExams.com

Study the graph carefully and answer the question given below it.
The import in $$1976$$ was approximately how many times that of the year $$1971$$?
313161.png
  • $$0.31$$
  • $$1.68$$
  • $$2.41$$
  • $$3.22$$
Evaluate $$\displaystyle \frac{(a-b)^{2}}{(b-c)(c-a)}+\frac{(b-c)^{2}}{(a-b)(c-a)}+\frac{(c-a)^{2}}{(a-b)(b-c)}$$
  • 0
  • 1
  • 2
  • 3
The region represented by the inequation system $$x,  y\ge 0,  y\le 6,  x+y\le 3$$ is
  • Unbounded in first quadrant
  • Unbounded in first and second quadrants
  • Bounded in first quadrant
  • None of the above
$$z=30x+20y,x+y\le 8,x+2y\ge 4,6x+4y\ge 12,x\ge 0,y\ge 0$$ has
  • Unique solution
  • Infinitely many solution
  • Minimum at $$\left( 4,0 \right) $$
  • Minimum 60 at point $$\left( 0,3 \right) $$
An aeroplane can carry a maximum of $$200$$ passengers. A profit of Rs.$$1000$$ is made on each executive class ticket and a profit of Rs.$$600$$ is made on each economy class ticket. The airline reserves at least $$20$$ seats for executive class. However, at least $$4$$ times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of each type must be sold in order to maximize the profit for the airline. What is the maximum profit?
  • $$136000$$
  • $$1360000$$
  • $$13600$$
  • $$1360$$
For the LPP $$Minz={ x }_{ 1 }+{ x }_{ 2 }$$ such that inequalities
$$5{ x }_{ 1 }+10{ x }_{ 2 }\ge 0,        { x }_{ 1 }+{ x }_{ 2 }\le 1,        { x }_{ 2 }\le 4$$   and    $${ x }_{ 1 },{ x }_{ 2 }\ge 0$$
  • There is a bounded solution
  • There is no solution
  • There are infinite solutions
  • None of the above
Which inequality is represented by the graph at the right?
427588.png
  • $$y< 2x+1$$
  • $$y< -2x+1$$
  • $$y<\cfrac{1}{2}x+1$$
  • $$y< -\cfrac{1}{2}x+1$$
Observe the given chart and graph and answer the following: a girl is $$17$$ years old and $$160$$ cms tall. At the end of the growth period she is likely to be how tall

454987.JPG
  • $$160$$ cm
  • $$151$$ cm
  • $$160$$ m
  • $$151$$ m
A wholesale merchant wants to start the business of cereal with Rs. $$24000$$. Wheat is Rs. $$400$$ per quintal and rice is Rs. $$600$$ per quintal. He has capacity to store $$200$$ quintal cereal. He earns the profit Rs.$$25$$ per quintal on wheat and Rs. $$40$$ per quintal on rice. If he stores $$x$$ quintal rice and $$y$$ quintal wheat, then for maximum profit the objective function is
  • $$25x+40y$$
  • $$40x+25y$$
  • $$400x+600y$$
  • $$\dfrac{400}{40}x + \dfrac{600}{25}y$$
The fessible region of LPP is a convex polygon and its two consecutive vertices gives optimum solution the LPP has
  • Only one and finite solution
  • No solution
  • Two solutions
  • None of the above
A LPP means
  • Only objective function is linear
  • Only constraints are linear
  • Either objective function or constraints are linear
  • All objective function and constraints are linear
Vikas printing company takes fee of Rs. $$28$$ to print a oversized poster and Rs. $$7$$ for each colour of ink used. Raaj printing company does the same work and charges poster for Rs. $$34$$ and Rs. $$5.50$$ for each colour of ink used. If $$z$$ is the colours of ink used, find the values of $$z$$ such that Vikas printing company would charge more to print a poster than Raaj printing company.
  • $$z < 4$$
  • $$2 \leq z \leq 4$$
  • $$4 \leq z \leq 7$$
  • $$z > 4$$
If given constraints are $$5x + 4y \geq 2, x \leq 6, y \leq 7$$, then the maximum value of the function $$z = x + 2y$$ is
  • $$13$$
  • $$14$$
  • $$15$$
  • $$20$$
The constraints $$-{ x }_{ 1 }+{ x }_{ 2 }\le 1,\quad -{ x }_{ 1 }+3{ x }_{ 2 }\le 9$$ and $${ x }_{ 1 },{ x }_{ 2 }\ge 0$$ defines on
  • bounded feasible space
  • unbounded feasible space
  • both unbounded and bounded feasible space
  • None of the above
Shaded region is represented by
460963.jpg
  • $$2x+5y\ge 80,x+y\le 20,x\ge 0,y\le 0$$
  • $$2x+5y\ge 80,x+y\ge 20,x\ge 0,y\ge 0$$
  • $$2x+5y\le 80,x+y\le 20,x\ge 0,y\ge 0$$
  • $$2x+5y\le 80,x+y\le 20,x\le 0,y\le 0$$
$$\displaystyle z=10x+25y$$ subject to $$\displaystyle 0\le x\le 3$$ and $$\displaystyle 0\le y\le 3,x+y\le 5$$ then the maximum value of z is
  • $$80$$
  • $$95$$
  • $$30$$
  • $$75$$
A dealer wishes to purchase toys $$A$$ and $$B$$. He has Rs. $$580$$ and has space to store $$40$$ items. $$A$$ costs Rs. $$75$$ and $$B$$ costs Rs. $$90$$. He can make profit of Rs. $$10$$ and Rs.$$15$$ by selling $$A$$ and $$B$$ respectively assuming that he can sell all the items that he can buy formulation of this as L.P.P. is
  • Maximize $$\displaystyle z=10x+15y$$

    Subject to $$\displaystyle x+y\le 40,75x+90y\le 580,x\ge 0,y\ge 0$$
  • Maximize $$\displaystyle z=10x+15y$$

    Subject to $$\displaystyle x+y\ge 40,x\ge 0,y\ge 0,75x+90y\ge 580$$
  • Maximize $$\displaystyle z=15x+10y$$

    Subject to $$\displaystyle x+y\le 40,75x+90y\le 580,x\ge 0,y\ge 0$$
  • Maximize $$\displaystyle z=10x+15y$$

    Subject to $$\displaystyle x+y\ge 40,75x+90y\le 580,x\ge 0,y\ge 0$$
Given a system of inequation:
$$\displaystyle 2y-x\le 4$$
$$\displaystyle -2x+y\ge -4$$
Find the value of $$s$$, which is the greatest possible sum of the $$x$$ and $$y$$ co-ordinates of the point which satisfies the following inequalities as graphed in the $$xy$$ plane.
  • $$8$$
  • $$12$$
  • $$2$$
  • $$4$$
The maximum value of $$P=x+3y$$ such that $$2x+y\leq 20, x+2y\leq 20, x\geq 0, y\geq 0,$$ is.
  • $$50$$
  • $$40$$
  • $$30$$
  • None of these
For a linear programming equations, convex set of equations is included in region of
  • feasible solutions
  • disposed solutions
  • profit solutions
  • loss solutions
In linear programming, oil companies used to implement resources available is classified as
  • implementation modeling
  • transportation models
  • oil model
  • resources modeling
Linear programming used to optimize mathematical procedure and is
  • subset of mathematical programming
  • dimension of mathematical programming
  • linear mathematical programming
  • all of above
In transportation models designed in linear programming, points of demand is classified as
  • ordination
  • transportation
  • destinations
  • origins
Which of the following is a property of all linear programming problems?
  • alternate courses of action to choose from
  • minimization of some objective
  • a computer program
  • usage of graphs in the solution
  • usage of linear and nonlinear equations and inequalities
A furniture company makes one style of tables and chairs. The chart on the left above gives the prices of these tables and chairs in three different years. The chart on the right gives the maximum number of tables and chairs that can be stocked in each of three ware-houses, $$X, Y$$, and $$Z$$. Based on the prices shown, what was the maximum possible value of the table and chair inventory in warehouse $$Y$$ in 1995 ?

498302.png
  • $$\$23,950$$
  • $$\$26,500$$
  • $$\$27,200$$
  • $$\$28,400$$
  • $$\$29,500$$

In graphical solutions of linear inequalities, solution can be divided into
    • one subset
    • two subsets
    • three subsets
    • four subsets
    Linear programming model which involves funds allocation of limited investment is classified as
    • ordination budgeting model
    • capital budgeting models
    • funds investment models
    • funds origin models
    In linear programming, objective function and objective constraints are
    • solved
    • linear
    • quadratic
    • adjacent
    In order for a linear programming problem to have a unique solution, the solution must exist
    • at the intersection of the nonnegativity constraints.
    • at the intersection of a nonnegativity constraint and a resource constraint.
    • at the intersection of the objective function and a constraint.
    • at the intersection of two or more constraints.
    • none of the above
    The first step in formulating an LP problem is
    • graph the problem.
    • perform a sensitivity analysis.
    • identify the objective and the constraints.
    • define the decision variables.
    • understand the managerial problem being faced.
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