1.

For kind of cake requires 200 g of flour and 25 g of fat, another kind of cake requires 100 g of flour and 50 g of fat. Find the maximum number of cakes which can be made from 5 kg of flour and 1 kg of fat, assuming that there is no shortage of the other ingredients used in making the cakes. Make it an LLP and solve it fraphically.

Answer»


Solution :Let the number of cakes of the FIRST and second type be x and y respectively. Then we have to MAXIMISE `z=+y` subject to the constraints
`200x+100y,le5000implies2x+yle50""...(i)`
`25x+50yle100impliesx+2yle40""...(ii)`
and `x ge0,yge0.`

First we deaw the line `2x+y=50.`
For this, we plot the points `A(25,0),B(0,50) and C(10,30).` Draw the line ACB.
The region below this line represents `2x+y le50.`
Now, we draw the line `x+2y=40.`
For this, we plot the points `D(40,0),E(0.20)and F(20,10).` Draw the line DFE.
The region below this line represents `x+2y le40.`
The feasible regin CONTAINS the points `A(25,0),F(20,10) and E(0,20).`
Value of z at `A(25,0)=25+0=25.`
Value of z at `F(20,10)=20+10=30.`
Valus of z at `E(0,20)=0+20=20.`
For maximum value of z, we have x=20 and y=10. ltbr gt Maximum number of cakes REQUIRED for first and second type are 20 and 10 respectively.


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