You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Linear Programming Problems

One kind of c...

Question

One kind of cake requires $300 g m$ of flour and $15 g m$ of fat and another kind of cake requires $150 g m$ of flour and $30 g m$ of fat. Find the maximum number of cake that can be made from $7.5 k g$ of flour and $600 g m$ of fat . Form a linear programming problem and solve it graphically.

Open in App

Solution

Let $x$ and $y$ be the number of cake of first and second kind respectively.
Case I:- Given that first kind of cake requires $300 g$ of flour while the second kind of cake required $150 g$ of flour.
Maximum quantity available $= 7.5 k g = 7500 g$
Therefore,
$300 x + 150 y \leq 7500$
$2 x + y \leq 50; x \geq 0, y \geq 0$
$x$ $0$ $25$
$y$ $50$ $0$
Case II:- Given that first kind of cake requires $15 g$ of fat while second kind of cake required $30 g$ of fat.
Maximum quantity available $= 600 g$
Therefore,
$15 x + 30 y \leq 600$
$x + 2 y \leq 40; x \geq 0, y \geq 0$
$x$ $0$ $40$
$y$ $20$ $0$
Total no. of cakes $= x + y$
$M a x Z = x + y$
Corner points Value of $Z$
$(0, 20)$ $20$
$(20, 10)$ $30$
$(25, 0)$ $25$
Thus value of $Z$ is maximum when $x = 20$ and $y = 30$ , i.e.,
No. of cakes will be maximum when the no. of cakes of first and second kind are $20$ and $10$ respectively.
Hence the maximum no. of cakes that can be made are $30$ .

Suggest Corrections

Similar questions

Q. One kind of cake requires 300 gm of flour and 15 gm of fat, another kind of cake requires 150 gm of flour and 30 gm of fat. Find the maximum number of cakes which can be made from 7.5 kg of flour and 600 gm of fat, assuming that there is no shortage of the other ingradients used in making the cake. Make it as an LPP and solve it graphically.

Q. One kind of cake requires

300 g m

of flour and

15 g m

of fat and another kind of cake requires

150 g m

of flour and

30 g m

of fat. Find the maximum number of cake which can be made from

7.5 k g

of flour and

600 g m

of fat, assuming that there is no shortage of the other ingredients used in making the cakes. Make it as an

L . P . P

only.

Q. One kind of cake requires

200 g

of flour and

25 g

of fat, and another kind of cake requires

100 g

of flour and

50 g

of fat. Find the maximum number of cakes that can be made from

5 k g

of flour and

1 k g

of fat assuming that there is no shortage of the other ingredients used in making the cakes.

Q. One kind of cake requires 200 g of flour and 25 g of fat, and 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 storage of the other ingredients used in making the cakes.

One kind of cake requires 200 g of flour and 25 g of fat and 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.

Join BYJU'S Learning Program

Corner points	Value of $Z$
$(0, 20)$	$20$
$(20, 10)$	$30$
$(25, 0)$	$25$

One kind of cake requires 300gm of flour and 15gm of fat and another kind of cake requires 150gm of flour and 30gm of fat. Find the maximum number of cake that can be made from 7.5kg of flour and 600gm of fat . Form a linear programming problem and solve it graphically.

One kind of cake requires $300 g m$ of flour and $15 g m$ of fat and another kind of cake requires $150 g m$ of flour and $30 g m$ of fat. Find the maximum number of cake that can be made from $7.5 k g$ of flour and $600 g m$ of fat . Form a linear programming problem and solve it graphically.