Practice Test

Q1) In case of a linear programming problem, feasible region is always Show Answer

Q2) In linear programming proble, the linear function Z subject to certain conditions determined by a set of linear inequalities with variable as non-negative is Show Answer

Q3) A problem which seeks to maximise or minimise a linear function (say, of two variables x and y) subject to certain constraints as determined by a set of linear inequalities is called a/an Show Answer

Q4) Consider the following statements: I. The term linear implies that all mathematical relations used in the problem are linear relations. II. The term programming refers to the method of determining a particular programme. Choose the correct option. Show Answer

Q5) A furniture dealer deals in only two items-tables and chairs. He has Rs. 50,000 to invest and has storage space of atmost 60 pieces. A table costs Rs. 2,500 and a chair Rs. 500. Then, the constraints of the above problem are (where x is number of tables and y is number of chairs) Show Answer

Q6) If a furniture dealer estimates that from the sale of one table he can make a profit of Rs. 250 and from the sale of one chair of a profit of Rs. 75 and if x is the number of chairs and y is the number of tables, then its linear objective function is Show Answer

Q7) Which of the following is a liner objective function? Show Answer

Q8) The variable x and y in a liner programming problem are called Show Answer

Q9) Which of the following statements is false? Show Answer

Q10) The objective function of an LPP is Show Answer

Q11) Which of the following sets are not convex? Show Answer

Q12) An optimisation problem may involve finding Show Answer

Q13) If a young man rides his motorcycle at 25 km/h, he has to spend Rs. 2 per km in petrol and if he rides it at 40 km/h, the petrol cost rises to Rs. 5 per km. He has Rs. 100 to spend on petrol and wishes to find the maximum distance, he can travel within one hour. If x and y denote the distance traveled by him (in km) at 25 km/h and 40 km/h, respectively. The in-equations represent the data are Show Answer

Q14) Priya has to stitch table clothes and curtains for a living. She has to put in 1 hour of work for a table cloth and 3 hours for a curtain. She gets Rs. 50 for every table cloths and Rs. 250 for every curtain. She has to earn a least Rs. 500 per day. Minimize the no. of hours of work she has to put in every day. Show Answer

Q15) Which of the following cannot be considered as the objective function of a linear programming problem? Show Answer

Q16) Find the linear inequations for which the shaded area in following figure is the soultion set: Show Answer

Q17) The corner point method for bounded feasible region comprises of the following steps:
I. When the feasible region is bounded, M and m are the maximum and minimum values of Z.
II. Find the feasible region of the linear programming problem and determine its corner points.
III. Evaluate the objective function Z = a x + b y at each corner point. Let M and m respectively be the largest and smallest values of these points. The correct order of these above steps is Show Answer

Q18) Maximum of Z occurs at Show Answer

Q19) Minimum of Z occurs at Show Answer

Q20) (Maximum value of Z + Minimum value of Z) is equal to Show Answer

Q21) A toy manufacturer produces two types of dolls; a basic version doll A and a deluxe version doll B. Each doll of type B takes twice as long to produce as one doll of type A. The company have time to make a maximum of 2000 dolls of type A per day, the supply of plastic is sufficient to produce 1500 dolls per day and each type requires equal amount of it. The deluxe version, i.e. type B requires a fancy dress of which there are only 600 per day available. If the company makes a profit of Rs. 3 and Rs. 5 per doll, respectively, on doll A and B, then the number of each should be produced per day in order to maximise profit, is Show Answer

Q22) Let R be the feasible region (convex polygon) for a linear programming problem and Z = a x + b y be the objective function. Then, which of the following statements is false? Show Answer

Q23) Let the feasible region of the linear programming problem with the objective function Z = a x + b y is unbounded and let M and m be the maximum and minimum value of Z, respectively. Now, consider the following statements :
I. M is the maximum value of Z, if the open half plane determined by a x + b y > M has no point in common with the feasible region. Otherwise, Z has no maximum value.
II. m is the minimum value of Z, if the open half plane determined by a x + b y < m has no point in common with the feasible region. Otherwise, Z has no minimum value. Choose the correct option. Show Answer

Q24) Consider the following statements:
I. If the feasible region of an LPP is unbounded, then maximum or minimum value of the objective function Z = a x + b y may or may not exist.
II. Maximum value of the objective function Z = a x + b y in an LPP always occurs at only one corner point of the feasible region.
III. In an LPP, the minimum value of the objective function Z = a x + b y is always 0, if origin is one of the corner point of the feasible region.
IV. In an LPP, the maximum value of the objective function Z = a x + b y is always finite.
Which of the following statements are true? Show Answer

Q25) The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let Z = p x + q y, where p, q > 0. Then, the condition on p and q so that the maximum of Z occurs at both the points (15, 15) and (0, 20), is Show Answer

Q26) A cooperative society of farmers has maximum of 50 hectare of land to grow two crops X and Y. The profit from crops X and Y per hectare are estimated as Rs. 10500 and Rs. 9000, respectively. To control weeds, a liquid herbicide has to be used for crops X and Y at rates of 20 L and 10 L per hectare. Further no more than 800 L of herbicide should be used in order to protect fish and wildlife using a pond which collects drainage from his land. To maximise the total profit of the society, the land should be allocated to each crop is Show Answer

Q27) Anil wants to invest atmost Rs. 12000 in bonds A and B. According to the rules, he has to invest atleast Rs. 2000 in bond A and atleast Rs. 4000 in bond B. If the rate of interest in bond A is 8% per annum and on bond B is 10% per annum, then to maximise the interest, the investment in bond A and B are respectively Show Answer

Q28) 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 qunital. 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 Show Answer

Q29) Which of the term is not used in a linear programming problem? Show Answer