Linear Programming Problem in Management Mathematics

Solve the following using graphical method : 

Minimize :Z=3x+5y

`2x+3x>=12` 

`-x+y<=3` 

`x<=4,y>=3,x>=0,y>=0` 

Mr. Rajesh has ₹ 1800 to spend on fruits for a meeting. Grapes cost ₹ 160/kg llnd peaches ₹ 200/kg. Let x and g represent the number of kilogrames of grapes and peaches he can buy. Write the graph of an inequation to model the amounts of grapes and peaches he can buy within his budget. 

Minimize: Z = 2x + y 

Subject to: x + y ≤ 5 

x + 2y ≤  8 

4x + 3y ≥ 12 

x ≥  o,  y ≥ o 

Solve graphically.

Diet for a sick person must contain at least 4000 units of vitamins, 50 units of minerals and 1500 calories Two foods F₁ and F₂ cost Rs. 50 and Rs. 75 per unit respectively. Each unit of food F₁ contains 200 units of vitamins, 1 unit of minerals and 40 calories, whereas each unit of food F₂ contains 100 units of  vitamins, 2 units of minerals and 30 calories. Formulate the above problem as L.P.P. to satisfy the sick person's requirements at minimum cost.

A person makes two types of gift items A and B requiring the services of a cutter and a finisher.  Gift item A requires 4 hours of the cutter's time and 2 hours of finisher's time. Fifth item B requires 2 hours of the cutter's time and 4 hours of finisher's time. The cutter and finisher have 208 hours and 152 hours available time respectively every month. The profit on one gift item of type A is ₹ 75 and on one gift item of type, 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?

Find the graphical solution for the following system of linear equations :

3x + 4y ≥ 12 , 4x + 7y ≤ 28 , y ≥ 1 , x ≥ 0 , y ≥ 0 ,

Hence find the co-ordinates of comer points of the common region. 

Compute CDR using the information given below :

Total number of deaths in a year is given to be 900.

Solve the following L.P.P.:

Maximize Z = 4x + 5y
subject to       2x + y ≥ 4
                       x + y ≤ 5,
                       0 ≤ x ≤ 3,
                       0 ≤ y ≤ 3