Linear Programming Problem in Management Mathematics

Calculate the CDR for District A and B and compare them: 

There are found jobs to be completed. Each job must go through machines M₁ , M₂ , M₃ in the order M₁ - M₂ - M₃.  Processing time in hours is given below. Determine the optimal sequesnce and idle time for machine M₁ .

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.

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. : 
Minimize : Z = 4x + 10y, 
Subject to : 2x + 5y ≤10 , 5x + 3y ≤ 15, 
                  x + 2y  ≥ 30, x ≥ 0, y ≥ 0. 

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.