Q. 94.0( 2 Votes )

One kind of cake

Answer :

The above information can be expressed in the form of the following table



Let ‘x’ and ‘y’ units of cake 1 and cake 2 be made.


Number of cakes made = x + y


Now,


300x + 150y ≤ 7500


i.e. the maximum availability of flour is 7500g for both cakes, each of which requires 300g and 150g of flour respectively


15x + 30y ≥ 600


i.e. the maximum availability of fat is 600g for both the cakes, each of which requires 15g and 30g of fat.


Hence , mathematical formulation of the LPP is as follows :


Find ‘x’ and ‘y’ that,


Maximises Z = x + y


Subject to the following constraints:


(i) 300x + 150y ≤ 7500


i.e. 2x + y ≤ 50


(ii) 15x + 30y ≥ 600


i.e. x + 2y ≥ 40


(iii) x,y ≥0 ( quantity cant be negative)



The feasible region is bounded (ABO)


The corner points of the feasible region is as follows:



Z is maximised at B(20,10)


The maximum number of cakes that can be made are 20 and 10 of each kind i.e. 30 in total.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Corner points of Mathematics - Exemplar

Using the method Mathematics - Board Papers

Refer to ExerciseMathematics - Exemplar

A dietician wisheRD Sharma - Volume 2

A merchant plans Mathematics - Board Papers

A dietician wisheMathematics - Board Papers

Maximise and MiniMathematics - Exemplar