To Maximize profits, 2 batches of bread and 16 batches of muffins must be baked.
This is a problem of Linear Programming since we need to maximize profits subject to the time constraint of preparing and baking the goods.
Let Z be the objective function, i.e the profit earned
Let x and y be the batches of bread and muffins baked respectively.
It is given that each batch of bread makes a profit of $35 and each batch of muffins makes a profit of $10
The objective function will be
Z = 35x + 10y
where, x, y > 0
The time taken to prepare bread and muffin is 240 and 30 mins respectively. The time available for the preparation is 960 minutes.
Hence the total time to actually prepare must be less than or equal to 960 mins. Hence we got our first constraint
240x + 30y ≤ 960
Similarly, it takes 60 minutes and 30 minutes to bake bread and muffins respectively. The baking time available is 600 mins.
Hence, the second constraint is
60x + 30y ≤ 600
Hence the LPP formed is
Max Z = 35x + 10y
where, x, y > 0
240x + 30y ≤ 960
60x + 30y ≤ 600
Hence we will now plot the constraints as shown in the graph below.
This gives us 4 corner points
Now if we evaluate the value of Z for all 4 corner points we get
A (2,16) 35 X 2 + 10 X 16 = 230
B (0,20) 35 X 0 + 10 X 20 = 200
C (4,0) 35 X 4 + 10 X 0 = 140
D (0,0) 35 X 0 + 10 X 0 = 0
As we can clearly see the maximum value generated is from A (2, 16.) Hence this gives us the value for which the profit is maximum.
= 2 batches of bread and 16 batches of muffins
To learn more about LPP visit
https://brainly.com/question/27580242
#SPJ4
