Question

A company makes two types of biscuits: Jumbo and Regular. The oven can cook at most 200 biscuits per day. Each jumbo biscuit requires 2oz of flour, each regular biscuit requires 1oz of flour, and there is 300oz of flour available. The income from each jumbo biscuit is $0.09 and from each regular biscuit is $0.14. How many of each size biscuit should be made to maximize income? What is the maximum income?*Answer setup *The company should make [__] jumbo and [___] regular biscuits.The maximum income is [___].

Answer 1

For this case we can do the following:

x= number of jumbo biscuits

y= number of regular biscuits

Then we can write the conditions given:

1) For the total of biscuits in a day we have

`x+y\le200`

2) For the amount of flour we have:

`2x+y\le300`

3) And we need to satisfy these other conditions:

`x\ge0,y\ge0`

After this we have an objective function associated to the totat income and we can write:

`IC=0.09x+0.14y`

Now we need to plot the conditions to find the optimal solution:

We have 4 possible points as the solution :

(0,0) (0,200), (100,100), (150,0)

Now we evaluate the objective function for each point and we got:

IC(0,0)= 0.09*0 +0.14*0 = 0

IC(0,200)= 0.09*0 +0.14*200 = 28

IC(100,100)= 0.09*100 +0.14*100 = 23

IC(150,0)= 0.09*150 +0.14*0 = 13.5

Since we want to maximize the income then the optimal solution would be 0 jumbo buscuits and 200 normal biscuits

And the maximum income is 28

The company should make 0 jumbo and 200 regular biscuits.

The maximum income is 28.​