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.

Mr. Wood's construction class at CHSW is going to be building tool sheds this year and then selling them to the public to raise money for their program. They need 10 sheets of dry wall and 15 studs to build a small shed, and 15 sheets of dry wall and 45 studs to build a large shed. The principal told Mr. Wood's that he has 60 sheets of dry wall and 135 studs available for his students to use. If the school makes a $390 profit on a shed and $520 on a large shed, how many of each type of shed should the students build in order to maximize their profits?

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.

Mr. Wood's construction class at CHSW is going to be building tool sheds this year and then selling them to the public to raise money for their program. They need 10 sheets of dry wall and 15 studs to build a small shed, and 15 sheets of dry wall and 45 studs to build a large shed. The principal told Mr. Wood's that he has 60 sheets of dry wall and 135 studs available for his students to use. If the school makes a $390 profit on a shed and $520 on a large shed, how many of each type of shed should the students build in order to maximize their profits?

hero · Answer

Okay, you should be able to solve this one on your own.

hero · Answer

I showed you step by step how to do the previous two. Now it's your turn.

firejay5 · Answer

aww really come on

hero · Answer

Sorry to tell you the truth but I'm here to help students. I'll help you with the first couple problems. Then after that, it's your turn.

hero · Answer

That's the way I've always done it.

firejay5 · Answer

I need help on the maximization

hero · Answer

0. Given
Small Shed = 10 sheets of dry wall, 15 studs per
Large Shed = 15 sheets of dry wall, 45 studs per
Materials Available: 60 sheets of dry wall, 135 studs

1. Define variables

x = no. of small shed built
y = no. of large sheds built

2. Write Relevant Equations/Inequalities
Drywall = 10x + 15y <= 60
Studs    = 15x + 45y <= 135
Profit    = 390x + 520y 

Solve systems of inequalities for x and y
10x + 15y <= 60
15x + 45y <= 135

5(2x + 3y) <= 5(12)
  2x + 3y <= 12

15(x + 3y) = 15(9)
    x + 3y <= 9

3y <= 12 - 2x
3y <= 9 - x

0 <= 3 - x
x <= 3
y <= 2

Therefore, you need to make at least 3 Small Sheds and 2 Large Sheds in order to gain max profit. 

Now, find out how much Profit the school made:
P(x,y) = 390x + 520y 
P(x,y) = 390(3) + 520(2)
P(x,y) = 1170 + 1040
P(x,y) = 2210

The school made $2210 (max)

hero · Answer

This was not an easy one. This question would stump many

firejay5 · Answer

where's #"s 3 - 5

hero · Answer

Sorry. Once again, I provided the solution. You have to be able to decipher it

firejay5 · Answer

okay