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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