Linear Programming — practice questions
53 curated practice questions from Linear Programming (Mathematics Class 12, CBSE) — 2 hard, 45 easy, 6 medium. Every question includes the final answer free; step-by-step worked solutions with a free account.
- A company has two factories located at P and Q and has three depots situated at A , B and C . The weekly requirement of…
- Z = 4 x 1 + 5 x 2 , subject to 2 x 1 + x 2 ≥ 7, 2 x 1 + 3 x 2 ≤ 15, x 2 ≤ 3, x 1 , x 2 ≥0 The minimum value of Z occurs…
- A factory owner wants to purchase two types of machines, A and B , for his factory. The machine A requires an area of…
- Z = 8 x + 10 y , subject to 2 x + y ≥ 7, 2 x + 3 y ≥15, y ≥ 2, x ≥ 0, y ≥ 0 The minimum value of Z occurs at
- A furniture manufacturer produces tables and bookshelves made up of wood and steel. The weekly requirement of wood and…
- Region represented by x ≥ 0 y ≥ 0 is
- Kellogg is a new cereal formed of a mixture of bran and rice that contains at least 88 grams of protein and at least 36…
- A printing company prints two types of magazine A and B . The company earn ` 20 and ` 30 on each copy of magazines A…
- A shopkeeper sells two items, colour T.V. sets and DVD players. He can invest ` 12,00,000 and can store only 750 items…
- Maximize Z = 4 x + 6 y , subject to 3 x + 2 y ≤ 12, x + y ≥ 4, x , y ≥ 0
- Maximize Z = 10 x 1 + 25 x 2 , subject to 0 ≤ x 1 ≤ 3, 0 ≤ x 2 ≤ 3, x 1 + x 2 ≤ 5
- Two different kinds of foods A and B are being considered to form a weekly diet. The minimum weekly requirement of…
- A dealer wishes to purchase a number of fans and sewing machines. He has only ` 5760 to invest and has space for at…
- Corner points of the feasible region determined by the system of linear constraints are (0, 3), (1, 1) and (3, 0). Let…
- Maximize Z = 3 x + 5 y , subject to x + 4 y ≤ 24, 3 x + y ≤ 21, x + y ≤ 9, x ≥ 0, y ≥ 0
- The minimum value of Z = 4 x + 3 y subjected to the constraints 3 x + 2 y ≥ 160, 5 x + 2 y ≥ 200, x + 2 y ≥ 80; x , y ≥…
- Solution set of the inequality x ≥ 0 is
- An oil company requires 13,000, 20,000 and 15,000 barrels of high grade, medium grade and low grade oil respectively…
- In solving the LPP : “minimize f = 6 x + 10 y subject to constraints x ≥ 6, y ≥ 2, 2 x + y ≥ 10, x ≥ 0, y ≥ 0”…
- The region represented by the inequalities x ≥ 6, y ≥ 2, 2 x + y ≤ 10, x ≥ 0, y ≥ 0 is
- Two tailors P and Q earn ` 350 and ` 450 per day respectively. Tailor P can stitch 6 shirts and 3 trousers while tailor…
- Minimize Z = 20 x 1 + 9 x 2 , subject to x 1 ≥ 0, x 2 ≥ 0, 2 x 1 + x 2 ≥ 36, 6 x 1 + x 2 ≥ 60
- The objective function Z = 4 x + 3 y can be minimum subjected to the constraints 3 x + 4 y ≤ 24, 8 x + 6 y ≤ 48, x ≤ 5…
- A man has ` 1500 for purchase of rice and wheat. A bag of rice and a bag of wheat cost ` 180 and ` 120 respectively. He…
- The feasible region for a LPP is shown shaded in the figure. Let Z = 3 x – 4 y be the objective function. Minimum of Z…
- A factory makes two types of biscuits B 1 and B 2 that cost ` 145 and ` 160 per kg respectively. The minimum quantities…
- Z = 7 x + y , subject to 5 x + y ≥ 5, x + y ≥ 3, x ≥ 0, y ≥ 0 The minimum value of Z occurs at
- Maximize Z = 6 x + 4 y , subject to x ≤ 2, x + y ≤ 3, – 2 x + y ≤ 1, x ≥ 0, y ≥ 0
- An aeroplane can carry a maximum of 250 passengers. A profit of ` 1500 is made on each executive class ticket and a…
- The feasible region for an LPP is shown shaded in the figure. Let F = 3 x – 4 y be the objective function, then maximum…
- Maximize Z = 7 x + 11 y , subject to 3 x + 5 y ≤ 26, 5 x + 3 y ≤ 30, x ≥ 0, y ≥ 0
- Shamali wants to invest ` 50,000 in saving certificates and PPF. She wants to invest atleast ` 15, 000 in saving…
- Feasible region for an LPP is shown shaded in the following figure. Minimum of Z = 4 x + 3 y occurs at the point
- The corner points of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40)…
- Diet of sick person must contain atleast 4000 units of vitamins, 50 units of minerals and 2500 calories. Two foods F 1…
- If a motorcyclist rides at a speed of 50 km/hr, he has to spend ` 2 per km on petrol. If he rides at a faster speed of…
- Z = 6 x 1 + 2 x 2 , subject to 5 x 1 + 9 x 2 ≤ 90, x 1 + x 2 ≥ 4, x 2 ≤ 8, x 1 ≥ 0, x 2 ≥ 0 The minimum value of Z…
- A company manufactures two types of chemicals A and B . Each chemical requires two types of raw material P and Q . The…
- The maximum value of Z = 3 x + 2 y , subjected to x + 2 y ≤ 2, x + 2 y ≥ 8; x , y ≥ 0 is
- Z = 6 x + 21 y , subject to x + 2 y ≥ 3, x + 4 y ≥ 4, 3 x + y ≥ 3, x ≥ 0, y ≥ 0 The minimum value of Z occurs at
- Z =20 x 1 + 20 x 2 , subject to x 1 ≥ 0, x 2 ≥ 0, x 1 + 2 x 2 ≥ 8, 3 x 1 + 2 x 2 ≥ 15, 5 x 1 + 2 x 2 ≥ 20 The minimum…
- A dealer wishes to purchase table fans and ceiling fans. He has ` 57, 600 to invest, and has space to store 40 items. A…
- The maximum value of f = 4 x + 3 y subject to constraints x ≥ 0, y ≥ 0, 2 x + 3 y ≤ 18; x + y ≥ 10 is
- Corner points of the feasible region for an LPP are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). Let F = 4 x + 6 y be the…
- Maximize Z =11 x + 8 y , subject to x ≤ 4, y ≤ 6, x + y ≤ 6, x ≥ 0, y ≥ 0
- A shopkeeper deals in two items-thermos flasks and air tight containers. A flask costs him ` 120 and an air tight…
- A manufacturer produces two types of steel trunks. He has two machines A and B . The type P of the trunk requires 3…
- Refer to Q. 2. (Maximum value of Z + Minimum value of Z ) is equal to
- A manufacturer makes two products, A and B . Product A sells at ` 200 per unit and takes 30 minutes to make. Product B…
- The optimal value of the objective function is attained at the points
- The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15)…
- A company has factories located at each of the two places P and Q . From these locations, a certain commodity is…
- A brick manufacturer has two depots A and B , with stocks of 30000 and 20000 bricks respectively. He receives orders…