Question

For each problem, you must:
1. Define the variables
2. Write the function to be maximized or minimized.
3. Write a system of inequalities.
4. Graph and write the vertices of the feasible region.
5. Solve the problem and answer the question.

The Conway High Band is selling caramel and crunch bars to raise money for their trip to Florida in 2012. The caramel bars are packaged 20 bars per case. They pay $30 per case of caramel and make a profit of $17 per case. The crunch bars are packaged 24 bars per case and CHS pay $26 per case and makes a profit of $15 per case. They order no more than 3,000 caramel and crunch bars together and spend nor more than $4,000. How many cases of caramel and crunch bars would Mr. Cunningham need to buy to maximize their profits?

Answer 1

i am weak at it

Answer 2

No, never do that. Only post one question at a time. You can close this question now and post a new open question that I'm already here if you want.

Answer 3

can you view 2 questions at a time

Answer 4

You can close this question and open another question. I will work on this one. Someone else can at least look at the other one. If no one else helps with the other question, I can help with that too.

Answer 5

I need to have this done by today at least

Answer 6

1. Define Variables:
x = no of cases of caramel bars
y = no of cases of crunch bars

2. Write Associated Equations and Inequalities:

(Amount) 20x + 24y <= 3000
(Cost) 30x + 26y <= 4000
Profit) 17x + 15y = P(x,y)


3. Simplify each inequality and solve the system:
20x + 24y <= 3000
4(5x + 6y) <= 4(750)
5x + 6y <= 750

30x + 26y <= 4000
2(15x + 13y) <= 2(2000)
15x + 13y <= 2000

Write inequalities as a system:
5x + 6y <= 750
15x + 13y <= 2000

Multiply the first inequality by 3:
15x + 18y <= 2250
15x + 13y <=2000

Isolate 15x in each inequality:

15x <= 2250 - 18y
15x <= 2000 - 13y


Subtract the inequalities:
0 <= 250 - 5y

5y <= 250
y <= 250/5
y < = 50

Find x by substituting y back in:

15x + 13(50) <=2000
15x + 650 <= 2000
15 x <= 2000 - 650
15x <= 1350
x <= 90

Therefore the max values are x = 90, y = 50, meaning 90 caramel bar cases were bought and sold and 50 crunch bar cases were bought and sold

4: Use the Profit Equation to find the Total Profit:


P(x,y) = 17x + 15y
P(x,y) = 17(90) + 15(50)
P(x,y) = 2280

Therefore the total profit is $2280

5. Find the Total Cost using the Cost Function:
C(x,y) = 30x + 26y
C(x,y) = 30(90) + 26(50)
C(x,y) = 4000

Therefore the total cost was $4000, the maximum that could be spent.

Answer 7

@Hero What's #3

Answer 8

I wrote the solution to problem. It's up to you to decipher it.

Answer 9

so are there 3 functions to be maximized @Hero

Answer 10

Not exactly. System of inequalities was used to find the maximum values of the variables.

Answer 11

what's the function to be maximized

Answer 12

You want to maximize profit of course.

Answer 13

I cannot help you with every single category bro. Some things you have to be able to figure out yourself.

Answer 14

aww really

Answer 15

Sadly, yes. You need to be able to use your own thinking ability to figure out how to solve problems. Its unfortunate, but it is a reality of life. If you don't acquire the ability to do this, you may have some tough challenges facing you in life.

Answer 16

poopy

Answer 17

@Hero Where did you get 90 and 50