Q. 255.0( 2 Votes )

One kind of cake

Answer :

Let x be the number of cakes of the first kind, and y is of the second kind.

We can make a proper table for the given data.

By using this table, we can make LPP equations

Maximize = x + y

Equations are

300x + 150y≤7500

15x + 30y≤600

We can write these equations as:

2x + y≤50 - - - (i)

X + 2y≤40 - - - (ii)

And, x, y≥0

We can find the values of x and y , by put and check method

For equation (i) 2x + y≤50

For equation (ii) , X + 2y≤40

Now, we can draw the graph

Now, The feasible region is OCBAO .

The vertices of the feasible region are O(0, 0) , C(25, 50), B(20, 10) A(0, 20)

Point B is the intersection of the lines 2x + y = 50 and x + 2y = 40

Solving the equation, we get point P(20, 10)

And Maximum number of cakes = 30 at the point P(20, 10)

Hence, the first kind of cakes be 20 and the second kind of cakes be 10

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