Question

One cake requires 150 gm of flour and 50 gm of fat and another cake requires 75 gm of flour and fat.If bakery wants to make as many cakes as possible when 1.5 kg of flour and 0.5 kg of fat are available. How many at each kind should she make?​

Answer 1

Let number of first kind of cake is X and another kind of cake is Y.

So, total flour required =200X+100Y g

and total fat required =25X+50Y g

Since, maximum flour available is 5kg=5000g

∴200X+100Y≤5000

⇒2X+Y≤50 ...(1)

Also, maximum fat available is 1kg=1000g

∴25X+50Y≤1000

⇒X+2Y≤40 ...(2)

Since, quantity of cakes can't be negative.

∴X≥0,Y≥0 ...(3)

We have to maximize number of cakes that can be made.

So, Objective function is Z=X+Y

After plotting all the constraints given by equation (1), (2) and (3), we got the feasible region as shown in the image.

Corner points Value of Z=X+Y

A (0,20) 20

B (20,10) 30 (Maximum)

C (25,0) 25

So, maximum cake that can be made is 30, where first kind of cake will be 20 and second kind of cake will be 10.