CBSE Class 12 (Commerce) Linear Programming — practice questions
66 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice CBSE Class 12 (Commerce) Linear Programming in the app →Linear programming problems seek to maximise or:Linear programming is a class of which problems?The function to be maximised or minimised is the:The restrictions on the variables are called:The conditions x >= 0 and y >= 0 are called:The region satisfying all constraints is called:A point outside the feasible region is an:Points within and on the boundary of the feasible region are:Linear programming problems here are solved by which method?The optimal value of Z occurs at which points of the region?If the feasible region R is bounded, Z has:If the feasible region is unbounded, an optimum may:A feasible region is bounded if it can be:The region other than the feasible region is called:Theorem 1 describes the feasible region as a:Corner points of a feasible region are also called its:A linear programming problem must have constraints that are:Some problems minimise a linear function subject to given:What does the word programming mean in linear programming?A linear function Z = ax + by that has to be maximised or minimised is called what?In a linear programming problem, the conditions x ≥ 0 and y ≥ 0 are called what?The variables x and y in a linear programming problem are known as what?What is the common region determined by all the constraints of a linear programming problem called?What name is given to the part of the plane outside the feasible region?Which point of the feasible region is called an optimal solution?A dealer buys x tables at Rs 2500 and y chairs at Rs 500 with Rs 50,000 to invest. Which simplified constraintA dealer with storage for 60 pieces buys only chairs, each earning Rs 75 profit. What is his profit?A desk earns Rs 250 profit and a chair Rs 75. What is the profit on 10 desks and 50 chairs?Where must an optimal value of a linear objective function occur?What is guaranteed for Z = ax + by on a bounded feasible region?If the feasible region is unbounded, what can be said about the maximum or minimum of Z?What is the method of evaluating Z at the vertices of the feasible region called?Z = 250x + 75y has corner points (0,0), (20,0), (10,50), (0,60). Where is Z largest?A firm earns 4x + y while x + y ≤ 50, 3x + y ≤ 90 and x, y ≥ 0. What is its best Z?Cost 200x + 500y is kept low given x + 2y ≥ 10, 3x + 4y ≤ 24, x, y ≥ 0. Lowest cost?For Z = 3x + 9y, corner points (0,10), (5,5), (15,15), (0,20) are found. How many give the maximum?Two corner points give equal maximum Z. What holds between them?Minimise Z = 3x + 9y over corner points (0,10), (5,5), (15,15), (0,20). What is the minimum?On an unbounded region, when is the corner value m the minimum of Z?Minimise 3x + 2y with x + y ≥ 8, 3x + 5y ≤ 15, x, y ≥ 0. What happens?What is always true about the shape of the feasible region of a linear programming problem?Who formulated the transportation problem in 1941?The optimal diet problem was described in 1945 by which economist?In 1947 an efficient method for linear programming was suggested by which economist?Which event brought linear programming problems to the forefront for planning operations?Find the largest value of 3x + 4y when x + y ≤ 4 and neither x nor y is negative.Over x + 2y ≤ 8 and 3x + 2y ≤ 12 with x, y ≥ 0, find the least value of 4y - 3x.What is the greatest value of 5x + 3y if 3x + 5y ≤ 15, 5x + 2y ≤ 10 and x, y ≥ 0?A cost 3x + 5y must satisfy x + 3y ≥ 3 and x + y ≥ 2 with x, y ≥ 0. Least cost?Under x + 2y ≤ 10 and 3x + y ≤ 15 with x, y ≥ 0, how large can 3x + 2y become?Find the least value of x + 2y over the region 2x + y ≥ 3, x + 2y ≥ 6, x, y ≥ 0.Within x + 2y ≤ 120, x + y ≥ 60, x ≥ 2y and y ≥ 0, how large can 5x + 10y get?Can x + y be maximised when x - y ≤ -1 and y ≤ x with x, y ≥ 0? Pick the outcome.With x ≥ 3, x + y ≥ 5, x + 2y ≥ 6 and y ≥ 0, what happens when maximising 2y - x?On a bounded region, corner values M (largest) and m (smallest) represent what?What shape is the feasible region of a linear program in general n-dimensional space?Who published a method for solving systems of linear inequalities in 1827?Kantorovich and Koopmans shared which honour in 1975 for work related to linear programming?Who invented the simplex method in 1947, the first to tackle most linear programs efficiently?Who first showed in 1979 that linear programming can be solved in polynomial time?Which mathematician introduced a new interior-point method for linear programming in 1984?What is the dual of the dual of a linear program?How does the simplex algorithm move on the feasible polytope?The Klee and Minty family of problems showed what about the simplex algorithm?A primal maximises cTx with Ax ≤ b, x ≥ 0. What bound does its dual give?What was Dantzig's original example of a huge search space?