Linear Programming Maths - Linear Programming

The half plane represented by 4x + 3y > 14 contains the point _______.

The half plane represented by 3x + 2y < 8 contains the point _______.

If the corner points of the feasible solution are (0, 10), (2, 2) and (4, 0) then the point of minimum z = 3x + 2y is _______.

Sketch the graph of each of following inequations in XOY co-ordinate system. |x + 5| ≤ y

Sketch the graph of each of following inequations in XOY co-ordinate system. 2y – 5x ≥ 0

Sketch the graph of each of following inequations in XOY co-ordinate system. x + y≤ 0

Sketch the graph of each of following inequations in XOY co-ordinate system. x ≥ 5y

A company manufactures two types of toys A and B. Each toy of type A requires 2 minutes for cutting and 1 minute for assembling. Each toy of type B requires 3 minutes for cutting and 4 minutes for assembling. There are 3 hours available for cutting and 2 hours are available for assembling. On selling a toy of type A the company gets a profit of Rs.10 and that on toy of type B is Rs. 20. Formulate the L.P.P. to maximize profit.

Represent the solution set of inequation 3x + 2y ≤ 6 graphically.

Solve graphically : 5y + 3 ≤ 0

Solve graphically :3x + 4 ≤ 0

Solve graphically : 2y – 5 ≥ 0

Solve graphically :2x – 3 ≥ 0

A horticulturist wishes to mix two brands of fertilizers that will provide a minimum of 15 units of potash, 20 units of nitrate and 24 units of phosphate. One unit of brand I provides 3 units of potash, 1 unit of nitrate, 3 units of phosphate. One unit of brand II provides 1 unit of potash, 5 units of nitrate and 2 units of phosphates. One unit of brand I costs Rs. 120 and one unit of brand II costs Rs.60 per unit. Formulate this problems as L.P.P. to minimize the cost.

A Toy manufacturer produces bicycles and tricycles, each of which must be processed through two machine A and B. Machine A has maximum of 120 hours available and machine B has a maximum of 180 hours available. Manufacturing a bicycle requires 4 hours on machine A and 10 hours on machine B. Manufacturing a tricycle required 6 hours on machine A and 3 hours on machine B. If profits are Rs.65 for a bicycle and Rs.45 for a tricycle, formulate L.P.P. to have maximum profit.

Find the graphical solution of 3x + 4y ≤ 12, and x - 4y ≤ 4.

Find the common region of the solutions of the inequations x + 2y ≥ 4, 2x - y ≤ 6.

A firm manufacturing two types of electrical items A and B, can make a profit of ₹ 20/- per unit of A and ₹ 30/- per unit of B. Both A and B make use of two essential components a motor and a transformer. Each unit of A requires 3 motors and 2 transformers and each units of B requires 2 motors and 4 transformers. The total supply of components per month is restricted to 210 motors and 300 transformers. How many units of A and B should the manufacture per month to maximize profit? How much is the maximum profit?

A firm manufactures two products A and B on which profit earned per unit ₹3/- and ₹4/- respectively. Each product is processed on two machines M1 and M2. The product A requires one minute of processing time on M1 and two minute of processing time on M2, B requires one minute of processing time on M1 and one minute of processing time on M2. Machine M1 is available for use for 450 minutes while M2 is available for 600 minutes during any working day. Find the number of units of product A and B to be manufactured to get the maximum profit.

A person makes two types of gift items A and B requires the services of a cutter and a finisher. Gift item A requires 4 hours of cutter’s time and 2 hours of finisher’s time. B requires 2 hours of cutter’s time and 4 hours of finisher’s time. The cutter and finisher have 208 hours and 152 hours available times respectively every month. The profit of one gift item of type A is ₹ 75/- and on gift item B is ₹ 125/-. Assuming that the person can sell all the gift items produced, determine how many gift items of each type should he make every month to obtain the best returns?

A chemical company produces a chemical containing three basic elements A, B, C so that it has at least 16 liters of A, 24 liters of B and 18 liters of C. This chemical is made by mixing two compounds I and II. Each unit of compound I has 4 liters of A, 12 liters of B, 2 liters of C. Each unit of compound II has 2 liters of A, 2 liters of B and 6 liters of C. The cost per unit of compound I is ₹ 800/- and that of compound II is ₹ 640/-. Formulate the problem as L.P.P. and solve it to minimize the cost.

A company produces mixers and food processors. Profit on selling one mixer and one food processor is ₹ 2,000/- and ₹ 3,000/- respectively. Both the products are processed through three Machines A, B, C. The time required in hours by each product and total time available in hours per week on each machine are as follows :

How many mixers and food processors should be produced to maximize the profit?